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93-634: The society was founded in 1903 by Ludwig Boltzmann , Gustav von Escherich , and Emil Müller as Mathematical Society in Vienna ( German : Mathematische Gesellschaft in Wien ). After the Second World War it resumed operation in May 1946 and was formally reestablished at the 10th of August 1946 by Rudolf Inzinger . In autumn 1948 the name was changed to Austrian Mathematical Society . It publishes

186-903: A letter of recommendation written by Josef Stefan , Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria . In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876. In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She

279-702: A close relationship with Colloredo. In 1803, the archbishopric was secularised by Emperor Napoleon ; he transferred the territory to Ferdinando III of Tuscany , former Grand Duke of Tuscany , as the Electorate of Salzburg . In 1805, Salzburg was annexed to the Austrian Empire , along with the Berchtesgaden Provostry . In 1809, the territory of Salzburg was transferred to the Kingdom of Bavaria after Austria's defeat at Wagram . After

372-408: A deceptively simple appearance, since f can represent an arbitrary single-particle distribution function . Also, the force acting on the particles depends directly on the velocity distribution function  f . The Boltzmann equation is notoriously difficult to integrate . David Hilbert spent years trying to solve it without any real success. The form of the collision term assumed by Boltzmann

465-406: A gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but

558-521: A hub for southbound trains through the Alps into Italy . Salzburg Airport has scheduled flights to European cities such as Frankfurt , Vienna , London , Rotterdam , Amsterdam , Brussels , Düsseldorf , and Zürich , as well as Hamburg , Edinburgh and Dublin . In addition to these, there are numerous charter flights. In the main city, there is the Salzburg trolleybus system and bus system with

651-497: A large population of students. The name "Salzburg" was first recorded in the late 8th century. It is composed of two parts; the first being " Salz- " German for "salt" and the second being "-burg" from Proto-West-Germanic : *burg conveying the same meaning as Latin : oppidum , lit.   'fortified settlement, city' and not that of the New High German : Burg , lit. 'fortress'. The area of

744-489: A mathematical device and went on to show that the same could apply to continuous systems which might be seen as a forerunner to the development of quantum mechanics. One biographer of Boltzmann says that Boltzmann’s approach “pav[ed] the way for Planck.” The concept of quantization of energy levels became a fundamental postulate in quantum mechanics, leading to groundbreaking theories like quantum electrodynamics and quantum field theory . Thus, Boltzmann's early insights into

837-595: A popular essay A German professor's trip to El Dorado . In May 1906, Boltzmann's deteriorating mental condition described in a letter by the Dean as "a serious form of neurasthenia " forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as bipolar disorder . Four months later he died by suicide on 5 September 1906, by hanging himself while on vacation with his wife and daughter in Duino , near Trieste (then Austria). He

930-469: A professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck . They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig , on

1023-663: A promising young mathematician. It also awards smaller prizes for the best dissertation, diploma and high-school thesis in mathematics. This article about an organisation in Austria is a stub . You can help Misplaced Pages by expanding it . This article about a mathematics organization is a stub . You can help Misplaced Pages by expanding it . Ludwig Boltzmann Ludwig Eduard Boltzmann ForMemRS ( / ˈ b ɒ l t s m ə n / , US also / ˈ b oʊ l -, ˈ b ɔː l -/ , Austrian German: [ˈluːdvɪɡ ˈbɔltsman] ; 20 February 1844 – 5 September 1906)

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1116-551: A systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations , the fluctuation theorem , and other approaches instead. The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable")

1209-515: A total of more than 20 lines, and service every 10 minutes. Salzburg has an S-Bahn system with four Lines (S1, S2, S3, S11), trains depart from the main station every 30 minutes, and they are part of the ÖBB network. Suburb line number S1 reaches the world-famous Silent Night chapel in Oberndorf in about 25 minutes. In the 1960s, The Sound of Music , based on the true story of Maria von Trapp , who took up with an aristocratic family and fled

1302-481: Is buried in the Viennese Zentralfriedhof . His tombstone bears the inscription of Boltzmann's entropy formula : S = k ⋅ log ⁡ W {\displaystyle S=k\cdot \log W} . Boltzmann's kinetic theory of gases seemed to presuppose the reality of atoms and molecules , but almost all German philosophers and many scientists like Ernst Mach and

1395-399: Is comparatively high, mainly in the summer months. The specific drizzle is called Schnürlregen in the local dialect. In winter and spring, pronounced foehn winds regularly occur. Salzburg's official population significantly increased in 1935 when the city absorbed adjacent municipalities . After World War II , numerous refugees found a new home in the city. New residential space

1488-474: Is contributed to by heat, spatial separation, and radiation. Maxwell–Boltzmann statistics and the Boltzmann distribution remain central in the foundations of classical statistical mechanics. They are also applicable to other phenomena that do not require quantum statistics and provide insight into the meaning of temperature . He made multiple attempts to explain the second law of thermodynamics, with

1581-433: Is due to Boltzmann's view of the second law of thermodynamics. In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at

1674-409: Is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice , with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that

1767-418: Is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states. Ludwig Boltzmann's contributions to physics and philosophy have left a lasting impact on modern science. His pioneering work in statistical mechanics and thermodynamics laid

1860-544: Is problematic. Nevertheless, some new structures have been added: the Mozarteum at the Baroque Mirabell Garden (Architecture Robert Rechenauer), the 2001 Congress House (Architecture: Freemasons), the 2011 Unipark Nonntal (Architecture: Storch Ehlers Partners), the 2001 "Makartsteg" bridge (Architecture: HALLE1), and the "Residential and Studio House" of the architects Christine and Horst Lechner in

1953-461: Is the Boltzmann constant , and ln is the natural logarithm . W (for Wahrscheinlichkeit , a German word meaning " probability ") is the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system – the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to

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2046-577: Is the fourth-largest city in Austria . In 2020, it had a population of 156,852. The town is on the site of the Roman settlement of Iuvavum . Salzburg was founded as an episcopal see in 696 and became a seat of the archbishop in 798. Its main sources of income were salt extraction, trade, as well as gold mining. The fortress of Hohensalzburg , one of the largest medieval fortresses in Europe, dates from

2139-477: Is the reason why there are no churches built in the Rococo style. Sigismund von Schrattenbach continued with the construction of "Sigmundstor" and the statue of holy Maria on the cathedral square. With the fall and division of the former "Fürsterzbistum Salzburg" (Archbishopric) to Upper Austria , Bavaria (Rupertigau) and Tyrol (Zillertal Matrei) began a long period of urban stagnancy. This era didn't end before

2232-420: Is thus "the most improbable case conceivable...an infinitely improbable configuration of energy." Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled

2325-469: Is used to calculate Space Shuttle re-entry in the upper atmosphere. It is the basis for Neutron transport theory, and ion transport in Semiconductors . Boltzmann's work in statistical mechanics laid the groundwork for understanding the statistical behavior of particles in systems with a large number of degrees of freedom. In his 1877 paper he used discrete energy levels of physical systems as

2418-668: The Congress of Vienna with the Treaty of Munich (1816) , Salzburg was definitively returned to Austria, but without Rupertigau and Berchtesgaden, which remained with Bavaria . Salzburg was integrated into the Province of Salzach and Salzburgerland was ruled from Linz . In 1850, Salzburg's status was restored as the capital of the Duchy of Salzburg , a crownland of the Austrian Empire . The city became part of Austria-Hungary in 1866 as

2511-763: The Mönchsberg and Kapuzinerberg , which offer green relief within the city. Salzburg is approximately 150 km (93 mi) east of Munich , 281 km (175 mi) northwest of Ljubljana , Slovenia , and 300 km (186 mi) west of Vienna . Salzburg has about the same latitude as Seattle . Due to its proximity to the Austrian-German border, the greater Salzburg urban area has sometimes (unoffcially) been thought of as if it included contiguous parts of Germany: Freilassing (until 1923 known as Salzburghofen), Ainring and Piding . Public transport planning and multiple public transport lines stretch across

2604-496: The kinetic theory of gases based upon the Second law of thermodynamics . This was important because Newtonian mechanics did not differentiate between past and future motion , but Rudolf Clausius ’ invention of entropy to describe the second law was based on disgregation or dispersion at the molecular level so that the future was one-directional. Boltzmann was twenty-five years of age when he came upon James Clerk Maxwell 's work on

2697-523: The monasteries and the early carcass houses dominated the medieval city for a long time. The Cathedral of Archbishop Conrad of Wittelsbach was the largest basilica north of the Alps . The choir of the Franciscan Church , construction was begun by Hans von Burghausen and completed by Stephan Krumenauer , is one of the most prestigious religious gothic constructions of southern Germany. At

2790-518: The physical chemist Wilhelm Ostwald disbelieved their existence. Boltzmann was exposed to molecular theory by the paper of atomist James Clerk Maxwell entitled "Illustrations of the Dynamical Theory of Gases" which described temperature as dependent on the speed of the molecules thereby introducing statistics into physics. This inspired Boltzmann to embrace atomism and extend the theory. Boltzmann wrote treatises on philosophy such as "On

2883-466: The physics establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed

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2976-441: The "International Mathematical News" ( German : Internationale Mathematische Nachrichten ) with three issues per year (not to be confused with Mathematische Nachrichten , an unrelated mathematics journal). It was issued for the first time in 1947. It also publishes the mathematics journal Monatshefte für Mathematik in cooperation with Springer-Verlag . Every year it awards its main prize ( German : Förderungspreis ) to

3069-496: The 11th century. In the 17th century, Salzburg became a center of the Counter-Reformation , with monasteries and numerous Baroque churches built. Salzburg's historic center ( German : Altstadt ) is renowned for its Baroque architecture and is one of the best-preserved city centers north of the Alps. The historic center was enlisted as a UNESCO World Heritage Site in 1996. The city has three universities and

3162-470: The 250th anniversary of the birth of Wolfgang Amadeus Mozart , all 35 churches of Salzburg rang their bells after 8:00 p.m. (local time) to celebrate the occasion. Major celebrations took place throughout the year. As of 2017 Salzburg had a GDP per capita of €46,100, which was greater than the average for Austria and most European countries. Salzburg is on the banks of the River Salzach , at

3255-607: The 8th century as was customary for many communities and cities on European rivers. Hohensalzburg Fortress , the city's fortress was built on the site of a Roman fort in 1077 by Archbishop Gebhard, who made it his residence. It was greatly expanded during the following centuries. This site is not the site of the Roman castrum superius , which was located on the Nonnberg nearby. The state of Salzburg and its counties soon gained more and more influence and power within Bavaria due to

3348-521: The 8th-century saint with the city's rebirth, when around 696  CE , Bishop Rupert of Salzburg received the remains of the Roman town from Duke Theodo II of Bavaria as well as a castrum superius (upper castle) on the Nonnberg Terrace as a gift. In return he was to evangelize the east and south-east of the country of Bavaria. Rupert reconnoitred the river for the site of his basilica and chose Juvavum. He ordained priests and annexed

3441-464: The Boltzmann constant in honor of Boltzmann's contributions to statistical mechanics. The Boltzmann constant plays a central role in relating thermodynamic quantities to microscopic properties, and it is now a fundamental constant in physics, appearing in various equations across many scientific disciplines. Because the Boltzmann equation is practical in solving problems in rarefied or dilute gases, it has been used in many diverse areas of technology. It

3534-521: The Europark Shopping Centre. (Architecture: Massimiliano Fuksas ) Salzburg has twenty-four urban districts and three extra-urban populations. Urban districts ( Stadtteile ): Extra-urban populations ( Landschaftsräume ): Salzburg is a tourist favorite, with the number of visitors outnumbering locals by a large margin in peak times. In addition to Mozart's birthplace noted above, other notable places include: Old Town Outside

3627-569: The Old Town Greater Salzburg area Salzburg is a center of education and home to three universities, as well as several professional colleges and gymnasiums (high schools) . Salzburg Hauptbahnhof is served by comprehensive rail connections, with frequent east–west trains serving Vienna , Munich , Innsbruck , and Zürich , including daily high-speed ICE services. North–south rail connections also serve popular destinations such as Venice and Prague . The city acts as

3720-623: The attempts ranging over many areas. He tried Helmholtz 's monocycle model, a pure ensemble approach like Gibbs, a pure mechanical approach like ergodic theory, the combinatorial argument, the Stoßzahlansatz , etc. Most chemists , since the discoveries of John Dalton in 1808, and James Clerk Maxwell in Scotland and Josiah Willard Gibbs in the United States, shared Boltzmann's belief in atoms and molecules , but much of

3813-568: The beginning of the 9th century at the latest. The Marienkirche dates from 1139. The first use of the German name Salzburg, meaning Salt-Castle , can be traced back to 739  CE when the name was used in Willibald 's report on the organization of the Bavarian dioceses by Saint Boniface . The name derives from the barges carrying salt on the River Salzach , which were subject to a toll in

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3906-477: The behaviour of individual atoms and molecules. Although many chemists were already accepting the existence of atoms and molecules, the broader physics community took some time to embrace this view. Boltzmann's long-running dispute with the editor of a prominent German physics journal over the acceptance of atoms and molecules underscores the initial resistance to this idea. It was only after experiments, such as Jean Perrin's studies of colloidal suspensions, confirmed

3999-407: The border. The Köppen climate classification specifies Salzburg's climate as a humid continental climate (Dfb). However, with the −3 °C (27 °F) isotherm for the coldest month, Salzburg can be classified as having a four-season oceanic climate (Cfb) with significant temperature differences between seasons. Due to the location at the northern rim of the Alps, the amount of precipitation

4092-522: The capital city of the Federal State of Salzburg ( Land Salzburg ) and saw the Americans leave the area once Austria had signed a 1955 treaty re-establishing the country as a democratic and independent nation and subsequently declared its perpetual neutrality . In the 1960s, the city became the shooting location and setting of the family musical film The Sound of Music . On 27 January 2006,

4185-687: The capital of a crownland of the Austrian Empire. The nostalgia of the Romantic Era led to increased tourism. In 1892, a funicular was installed to facilitate tourism to Hohensalzburg Fortress . Following World War I and the dissolution of the Austro-Hungarian Empire, Salzburg, as the capital of one of the Austro-Hungarian territories, became part of the new German Austria . In 1918, it represented

4278-657: The cathedral, the bishop's residence north-west of the cathedral, the cathedral monastery on its south side, St Peter's monastery and the Frauengarten (probably after a former women's convent that was dissolved in 1583). Only during the 12th century did the civil settlement begin to spread into the Getreidegasse, the Abtsgasse (Sigmund Haffner-Gasse) and along the quay. Around 1280 the first city fortifications were created. The oldest known city law document dates from

4371-530: The city center as it is today along with many palaces. On 31 October 1731, the 214th anniversary of the 95 Theses , Archbishop Count Leopold Anton von Firmian signed an Edict of Expulsion, the Emigrationspatent , directing all Protestant citizens to recant their non-Catholic beliefs. 21,475 citizens refused to recant their beliefs and were expelled from Salzburg. Most of them accepted an offer by King Friedrich Wilhelm I of Prussia , travelling

4464-757: The city has been inhabited continuously since the Neolithic Age until the present. In the La Tène period it was an administrative centre of the Celtic Alums in the Kingdom of Noricum . After the Roman invasion in 15 BC, the various settlements on the Salzburg hills were abandoned, following the construction of the Roman city in the area of the old town. The recently created Municipium Claudium Juvavum

4557-745: The city's buildings, especially those around Salzburg railway station. Although the town's bridges and the dome of the cathedral were destroyed, much of its Baroque architecture remained intact. As a result, Salzburg is one of the few remaining examples of a town of its style. American troops entered the city on 5 May 1945 and it became the centre of the American-occupied area in Austria . Several displaced persons camps were established in Salzburg—among them Riedenburg, Camp Herzl (Franz-Josefs-Kaserne), Camp Mülln, Bet Bialik, Bet Trumpeldor, and New Palestine. After World War II, Salzburg became

4650-638: The city. Political opponents, Jewish citizens and other minorities were subsequently arrested and deported to concentration camps. The synagogue was destroyed. After Germany invaded the Soviet Union, several POW camps for prisoners from the Soviet Union and other enemy nations were arranged in the city. During the Nazi occupation, a Romani camp was built in Salzburg-Maxglan. It

4743-430: The collision term was " molecular chaos ", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure. Finally, in the 1970s E. G. D. Cohen and J. R. Dorfman proved that

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4836-508: The construction of the residential well. Giovanni Gaspare Zuccalli , by order of the same archbishop, created the Erhard and the Kajetan church in the south of the town. The city's redesign was completed with buildings designed by Johann Bernhard Fischer von Erlach , donated by Prince Archbishop Johann Ernst von Thun. After the era of Ernst von Thun, the city's expansion came to a halt, which

4929-497: The denominator account for indistinguishable particles in the same condition. Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete, although Boltzmann used this as a mathematical device with no physical meaning. An alternative to Boltzmann's formula for entropy, above, is the information entropy definition introduced in 1948 by Claude Shannon . Shannon's definition

5022-550: The distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution ), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles. This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space . (See Hamiltonian mechanics .) The first term on

5115-685: The end of the Gothic era Nonnberg Abbey , the Margaret Chapel in St Peter's Abbey , St George's Chapel, and the stately halls of the "Hoher Stock" in Hohensalzburg Fortress were constructed. Inspired by Vincenzo Scamozzi , Prince-Archbishop Wolf Dietrich von Raitenau began to transform the medieval town to the architectural ideals of the late Renaissance . Plans for a massive cathedral by Scamozzi failed to materialize upon

5208-430: The existence of atoms and molecules. Nevertheless, the validity and importance of his ideas were eventually recognized, and they have since become cornerstones of modern physics. Here, we delve into some aspects of Boltzmann's legacy and his influence on various areas of science. Boltzmann's kinetic theory of gases was one of the first attempts to explain macroscopic properties, such as pressure and temperature, in terms of

5301-578: The fall of the archbishop. A second cathedral planned by Santino Solari rose as the first early Baroque church in Salzburg. It served as an example for many other churches in Southern Germany and Austria . Markus Sittikus and Paris von Lodron continued to rebuild the city with major projects such as Hellbrunn Palace , the prince archbishop's residence, the university buildings, fortifications, and many other buildings. Giovanni Antonio Daria managed by order of Prince Archbishop Guido von Thun

5394-464: The flourishing salt mining and the wide-ranging missionary activities. In 996 Otto III, Holy Roman Emperor rented Archbishop Hartwig the market rights and minting rights (probably also the toll law). The first part of Hohensalzburg Fortress was built in 1077. A city judge was first mentioned in a document in 1120/30. On the left bank of the Salzach an extensive spiritual district was created with

5487-563: The fortress. It was besieged for three months in 1525. Eventually, tensions were quelled, and the city's independence led to an increase in wealth and prosperity, culminating in the late 16th to 18th centuries under the Prince Archbishops Wolf Dietrich von Raitenau , Markus Sittikus , and Paris Lodron . It was in the 17th century that Italian architects (and Austrians who had studied the Baroque style) rebuilt

5580-426: The foundation for some of the most fundamental concepts in physics. For instance, Max Planck in quantizing resonators in his Black Body theory of radiation used the Boltzmann constant to describe the entropy of the system to arrive at his formula in 1900. However, Boltzmann's work was not always readily accepted during his lifetime, and he faced opposition from some of his contemporaries, particularly in regards to

5673-702: The invitation of Wilhelm Ostwald . Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902. In 1903, Boltzmann, together with Gustav von Escherich and Emil Müller , founded the Austrian Mathematical Society . His students included Karl Přibram , Paul Ehrenfest and Lise Meitner . In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on natural philosophy were very popular and received considerable attention. His first lecture

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5766-405: The kinetic theory of gases which hypothesized that temperature was caused by collision of molecules. Maxwell used statistics to create a curve of molecular kinetic energy distribution from which Boltzmann clarified and developed the ideas of kinetic theory and entropy based upon statistical atomic theory creating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas. It

5859-477: The left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions. In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions . This first-order differential equation has

5952-794: The length and breadth of Germany to their new homes in East Prussia. The rest settled in other Protestant states in Europe and the British colonies in America. In 1772–1803, under archbishop Hieronymus Graf von Colloredo , Salzburg was a center of late Illuminism . Colloredo is known for being one of the main employers of Wolfgang Amadeus Mozart . Colloredo often had arguments with Mozart and he dismissed him by saying, Soll er doch gehen, ich brauche ihn nicht! (He should go; I don't need him!). Mozart left Salzburg for Vienna in 1781 with his family, although his father Leopold stayed back, as he had

6045-482: The manor of Piding . Rupert built a church at St. Peter on the site of today's cathedral and probably also founded the associated monastery and the Benedictine nunnery on Nonnberg for his relative Erentrude . Salzburg has been the seat of a diocesan bishop since 739  CE and an archbishopric since 798  CE . The first cathedral was built under Archbishop Virgil. The Franciscan Church existed since

6138-499: The middle of Salzburg's old town (winner of the architecture award of Salzburg 2010 ). Other examples of contemporary architecture lie outside the old town: the Faculty of Science building (Universität Salzburg – Architecture Willhelm Holzbauer ) built on the edge of free green space, the blob architecture of Red Bull Hangar-7 (Architecture: Volkmar Burgstaller ) at Salzburg Airport, home to Dietrich Mateschitz 's Flying Bulls and

6231-425: The most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded,

6324-402: The northern boundary of the Alps . The mountains to Salzburg's south contrast with the rolling plains to the north. The closest alpine peak, the 1,972‑metre-high Untersberg , is less than 16 km (10 mi) from the city center. The Altstadt , or "old town", is dominated by its baroque towers and churches and the massive Hohensalzburg Fortress . This area is flanked by two smaller hills,

6417-561: The old town), the "Lepi" (public baths in Leopoldskron ) (built 1964), and the original 1957 constructed congress-center of Salzburg, which was replaced by a new building in 2001. An important and famous example of the architecture of this era is the 1960 opening of the Großes Festspielhaus by Clemens Holzmeister . Adding contemporary architecture to Salzburg's old town without risking its UNESCO World Heritage status

6510-462: The only available option would be to measure and tabulate such quantities for various materials. Boltzmann was born in Erdberg, a suburb of Vienna into a Catholic family. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg . Boltzmann

6603-541: The period of promoterism ( Gründerzeit ) brought new life into urban development. The builder dynasty Jakob Ceconi and Carl Freiherr von Schwarz filled major positions in shaping the city in this era. Buildings of classical modernism and in particular, post-war modernism is frequently encountered in Salzburg. Examples are the Zahnwurzen house (a house in the Linzergasse ;22 in the right center of

6696-725: The quantization of energy levels had a profound influence on the development of quantum physics. In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz . He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899 . Numerous things are named in his honour. Salzburg Salzburg

6789-470: The question of the objective existence of processes in inanimate nature" (1897). He was a realist. In his work "On Thesis of Schopenhauer's", Boltzmann refers to his philosophy as materialism and says further: "Idealism asserts that only the ego exists, the various ideas, and seeks to explain matter from them. Materialism starts from the existence of matter and seeks to explain sensations from it." Boltzmann's most important scientific contributions were in

6882-536: The residual German-speaking territories of the Austrian heartlands. This was replaced by the First Austrian Republic in 1919, after the Treaty of Saint-Germain-en-Laye (1919) . The Anschluss (the occupation and annexation of Austria, including Salzburg, into Nazi Germany ) took place on 12 March 1938, one day before a scheduled referendum on Austria's independence. German troops moved into

6975-440: The same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are

7068-412: The second law of thermodynamics was a significant achievement, and he provided the current definition of entropy ( S = k B ln ⁡ Ω {\displaystyle S=k_{\rm {B}}\ln \Omega } ), where k B is the Boltzmann constant and Ω is the number of microstates corresponding to a given macrostate. Max Planck later named the constant k B as

7161-509: The system's energy, interpreted as a measure of the statistical disorder of a system. Max Planck named the constant k B the Boltzmann constant . Statistical mechanics is one of the pillars of modern physics . It describes how macroscopic observations (such as temperature and pressure ) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity ) to microscopic behavior, whereas, in classical thermodynamics ,

7254-514: The values of the Avogadro constant and the Boltzmann constant , convincing the world that the tiny particles really exist . To quote Planck , "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases ". This famous formula for entropy S is S = k B ln ⁡ W {\displaystyle S=k_{\mathrm {B} }\ln W} where k B

7347-495: The values of the Avogadro constant and the Boltzmann constant that the existence of atoms and molecules gained wider acceptance. Boltzmann's kinetic theory played a crucial role in demonstrating the reality of atoms and molecules and explaining various phenomena in gases, liquids, and solids. Statistical mechanics, which Boltzmann pioneered, connects macroscopic observations with microscopic behaviors. His statistical explanation of

7440-566: The various molecules. Boltzmann's paradigm was an ideal gas of N identical particles, of which N i are in the i th microscopic condition (range) of position and momentum. W  can be counted using the formula for permutations W = N ! ∏ i 1 N i ! {\displaystyle W=N!\prod _{i}{\frac {1}{N_{i}!}}} where i ranges over all possible molecular conditions, and where ! {\displaystyle !} denotes factorial . The "correction" in

7533-717: The year 1287. Independence from Bavaria was secured in the late 14th century. Salzburg was the seat of the Archbishopric of Salzburg , a prince-bishopric of the Holy Roman Empire . As the Reformation movement gained steam, riots broke out among peasants in the areas in and around Salzburg. The city was occupied during the German Peasants' War , and the Archbishop had to flee to the safety of

7626-532: Was Boltzmann who derived the first equation to model the dynamic evolution of the probability distribution Maxwell and he had created. Boltzmann's key insight was that dispersion occurred due to the statistical probability of increased molecular "states". Boltzmann went beyond Maxwell by applying his distribution equation to not solely gases, but also liquids and solids. Boltzmann also extended his theory in his 1877 paper beyond Carnot, Rudolf Clausius , James Clerk Maxwell and Lord Kelvin by demonstrating that entropy

7719-586: Was an Arbeitserziehungslager (work 'education' camp), which provided slave labor to local industry. It also operated as a Zwischenlager (transit camp), holding Roma before their deportation to German camps or ghettos in German-occupied territories in eastern Europe. Salzburg was also the location of five subcamps of the Dachau concentration camp . Allied bombing destroyed 7,600 houses and killed 550 inhabitants. Fifteen air strikes destroyed 46 percent of

7812-434: Was an Austrian physicist and philosopher . His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of thermodynamics . In 1877 he provided the current definition of entropy , S = k B ln ⁡ Ω {\displaystyle S=k_{\rm {B}}\ln \Omega } , where Ω is the number of microstates whose energy equals

7905-565: Was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace. In 1905, he gave an invited course of lectures in the summer session at the University of California in Berkeley , which he described in

7998-412: Was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions. Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation – his famous H-theorem . However the key assumption he made in formulating

8091-528: Was awarded the status of a Roman municipium in 45  CE and has become one of the most important cities of the now Roman province of Noricum . When the province of Noricum collapsed in 488 at the beginning of the migration period , part of the Romano-Celtic population remained in the country. In the 6th century they came under the rule of the Baiuvarii . The Life of Saint Rupert credits

8184-404: Was constructed for American soldiers of the postwar occupation and could be used for refugees when they left. Around 1950, Salzburg passed the mark of 100,000 citizens, and in 2016, it reached the mark of 150000 citizens. Salzburg is home to large German, Bosnian, Serbian, and Romanian communities. Largest groups of immigrants by 1 January 2021 : The Romanesque and Gothic churches ,

8277-651: Was developed to describe the dynamics of an ideal gas. ∂ f ∂ t + v ∂ f ∂ x + F m ∂ f ∂ v = ∂ f ∂ t | c o l l i s i o n {\displaystyle {\frac {\partial f}{\partial t}}+v{\frac {\partial f}{\partial x}}+{\frac {F}{m}}{\frac {\partial f}{\partial v}}={\frac {\partial f}{\partial t}}\left.{\!\!{\frac {}{}}}\right|_{\mathrm {collision} }} where ƒ represents

8370-529: Was home-schooled until the age of ten, and then attended high school in Linz , Upper Austria . When Boltzmann was 15, his father died. Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna . He received his doctorate in 1866 and his venia legendi in 1869. Boltzmann worked closely with Josef Stefan , director of the institute of physics. It was Stefan who introduced Boltzmann to Maxwell's work. In 1869 at age 25, thanks to

8463-504: Was intended for use in communication theory but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to factorials or Stirling's approximation . Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in Gibbs (see reference). The Boltzmann equation

8556-468: Was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On 17 July 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881). Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst . He spent 14 happy years in Graz and it

8649-599: Was there that he developed his statistical concept of nature. Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria , Germany in 1890. In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna. Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach , who became

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