- Ludwig Boltzmann
Infobox_Scientist

name = Ludwig Boltzmann

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image_width = 225px

caption = Ludwig Eduard Boltzmann (1844-1906)

birth_date = birth date|1844|2|20|mf=y

birth_place=Vienna ,Austrian Empire

death_date = death date and age|1906|9|5|1844|2|20|mf=y

death_place=Duino nearTrieste ,Italy (at that timeAustrian Empire )

residence =Austria ,Germany

nationality =Austria n

field =Physicist

work_institution =University of Graz University of Vienna University of Munich University of Leipzig

alma_mater =University of Vienna

doctoral_advisor =Josef Stefan

doctoral_students =Paul Ehrenfest Philipp Frank Gustav Herglotz Lise Meitner

known_for =Boltzmann's constant Boltzmann equation H-theorem Boltzmann distribution Stefan-Boltzmann law

prizes =

religion =

footnotes =**Ludwig Eduard Boltzmann**(February 20 ,1844 –September 5 ,1906 ) was anAustria nphysicist famous for his founding contributions in the fields ofstatistical mechanics andstatistical thermodynamics . He was one of the most important advocates foratomic theory when that scientific model was still highly controversial.**Biography****Childhood and education**Boltzmann was born in Vienna, then capital of the

Austrian Empire . His father, Ludwig George Boltzmann, was a tax official. His grandfather, who had moved to Vienna fromBerlin , was a clock manufacturer, and Boltzmann’s mother, Katharina Pauernfeind, was originally fromSalzburg . He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school inLinz ,Upper Austria . At age 15, Boltzmann lost his father.Boltzmann studied

physics at theUniversity of Vienna , starting in 1863. Among his teachers were Josef Loschmidt,Joseph Stefan ,Andreas von Ettingshausen and Jozef Petzval. Boltzmann received his PhD degree in 1866 working under the supervision of Stefan; his dissertation was on kinetic theory of gases. In 1867 he became aPrivatdozent (lecturer). After obtaining his doctorate degree, Boltzmann worked two more years as Stefan’s assistant. It was Stefan who introduced Boltzmann to Maxwell's work.**Academic career**In 1869, at age 25, he was appointed full Professor of Mathematical Physics at the

University of Graz in the province ofStyria . In 1869 he spent several months inHeidelberg working withRobert Bunsen andLeo Königsberger and then in 1871 he was withGustav Kirchhoff andHermann von Helmholtz in Berlin. In 1873 Boltzmann joined theUniversity 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 was refused permission to unofficially audit lectures, and Boltzmann advised her to appeal; she did, successfully. OnJuly 17 , 1876 Ludwig Boltzmann married Henriette von Aigentler; they had three daughters and two sons. Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz wereSvante Arrhenius andWalther Nernst ."Paul Ehrenfest (1880–1933) along with Nernst [,] Arrhenius, and Meitner must be considered among Boltzmann’s most outstanding students."—Citation

last = Jäger

first = Gustav

author-link =

last2 = Nabl

first2 = Josef

author2-link =

last3 = Meyer

first3 = Stephan

author3-link =

publication-date =

date = April 1999

title = Three Assistants on Boltzmann

periodical = [*http://www.springerlink.com/content/103001/?p=afebb6f1a46d4fdd97f04c8efbdaff6c&pi=0 Synthese*]

series = [*http://www.springerlink.com/humanities-social-sciences-and-law/ Humanities, Social Sciences and Law*]

edition = June 2006

publication-place =

place =

publisher = Springer Netherlands

volume = 119

issue = 1-2

pages = 69–84

url = http://www.springerlink.com/content/vq5443477m7w7782/

issn-print = 0039-7857

issn-online = 1573-0964

issn = 1573-0964

doi = 10.1023/A:1005239104047

oclc =

accessdate = 2008-06-09

journal = Synthese] "Walther Hermann Nernst visited lectures by Ludwig Boltzmann" [*http://chem.ch.huji.ac.il/history/nernst.htm*] ] He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature. In 1885 he became a member of the ImperialAustrian Academy of Sciences and in 1887 he became the President of theUniversity of Graz .Boltzmann was appointed to the Chair of Theoretical Physics at the

University of Munich inBavaria , Germany in 1890.In 1893, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.**Final years**However, Boltzmann did not get along with some of his colleagues in Vienna, particularly

Ernst Mach , who became a professor of philosophy and history of sciences in 1895. Thus in 1900 Boltzmann went to theUniversity of Leipzig , on the invitation ofWilhelm Ostwald . After the retirement of Mach due to bad health, Boltzmann came back to Vienna in 1902. His students included Karl Przibram,Paul Ehrenfest andLise Meitner .In Vienna, Boltzmann not only taught physics but also lectured on philosophy. Boltzmann’s lectures on natural philosophy were very popular, and received a considerable attention at that time. His first lecture 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.

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods, likely the symptoms of undiagnosed

bipolar disorder . He himself jestingly attributed his rapid swings in temperament to the fact that he was born during the night betweenMardi Gras andAsh Wednesday .Fact|date=July 2007 Meitner relates that those who were close to Boltzmann were aware of his bouts of severe depression and his suicide attempts.On

September 5 ,1906 , while on a summer vacation inDuino , nearTrieste , Boltzmann hanged himself during an attack of depression. He is buried in the VienneseZentralfriedhof ; his tombstone bears the inscription S=k. log W.**Philosophy**Boltzmann's kinetic theory of gases seemed to presuppose the reality of

atom s andmolecule s, but almost all German philosophers and many scientists likeErnst Mach and the physical chemistWilhelm Ostwald opposed their existence. During the 1890s Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use Hertz's theory that atoms were "Bilder", that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing real atoms, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the second law.Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some phyicists, including Mach's student,

Gustav Jaumann , interpreted Hertz to mean that all electromagnetic behavior was continuous as if there were no atoms and molecules and as if all physical behavior was ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics. After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis where most physicists seemed to reject atoms and he was not even invited to the physics section but was stuck in a section called "applied mathematics" he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms ofLamarck 's theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance. In 1905 Boltzmann corresponded extensively with the Austro-German philosopherFranz Brentano in hope of mastering philosophy better apparently so that he could refute its presence in science better, but he became discouraged about this approach as well. In the following year 1906 his mental condition became so bad that he had to resign his position. He committed suicide in September of that same year.**Physics**Boltzmann's most important scientific contributions were in

kinetic theory , including theMaxwell-Boltzmann distribution for molecular speeds in a gas. In addition,Maxwell-Boltzmann statistics and theBoltzmann distribution over energies remain the foundations of classical statistical mechanics. They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature.Much of the

physics establishment did not share his belief in the reality ofatom s andmolecule s — a belief shared, however, by Maxwell inScotland and Gibbs in theUnited States ; and by most chemists since the discoveries ofJohn Dalton in 1808. He 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 ofcolloid al suspensions (1908-1909) confirmed the values ofAvogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist.To quote Planck, "The

logarithm ic connection betweenentropy andprobability was first stated by L. Boltzmann in hiskinetic theory of gases" [*Max Planck, p. 119.*] This famous formula for entropy $S$ is [*The concept of*] [entropy was introduced byRudolf Clausius in 1865. He was the first to enunciate thesecond law of thermodynamics by saying that "entropy always increases".*An alternative is the information entropy definition introduced in 1948 by Claude Shannon. [*]*http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html*] It 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 tofactorial s orStirling's approximation . Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in Gibbs (see reference).:$S\; =\; k\; ,\; log\; W$

where $k$ = 1.3806505(24) × 10

^{−23}J K^{−1}is Boltzmann's constant, and thelogarithm is taken to the natural base $e$. $W$ is the "Wahrscheinlichkeit", the frequency of occurrence of amacrostate [*cite book|last=Pauli| first=Wolfgang| title=Statistical Mechanics|publisher=MIT Press|location=Cambridge|year=1973|isbn=0-262-66035-0, p. 21*] or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — number of (unobservable) "ways" the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules. Boltzmann’s paradigm was anideal 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:$W\; =\; N!;\; /\; ;\; prod\_i\; N\_i!$

where "i" ranges over all possible molecular conditions. ($!$ denotes

factorial .) The "correction" in the denominator is because identical particles in the same condition are indistinguishable. $W$ is called the "thermodynamic probability " since it is aninteger greater than one, while mathematical probabilities are alwaysnumber s between zero and one.The equation for $S$ is engraved on Boltzmann's tombstone at the Vienna

Zentralfriedhof — his second grave.**The Boltzmann equation**The Boltzmann equation was developed to describe the dynamics of an

ideal gas .:$frac\{partial\; f\}\{partial\; t\}+\; v\; frac\{partial\; f\}\{partial\; x\}+\; frac\{F\}\{m\}\; frac\{partial\; f\}\{partial\; v\}\; =\; frac\{partial\; f\}\{partial\; t\}left.\{!!frac\{\}\{\; ight|\_mathrm\{collision\}$

where $f$ represents 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 . (SeeHamiltonian mechanics .) The first term on 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-orderdifferential equation has a deceptively simple appearance, since $f$ can represent an arbitrary single-particle distribution function. Also, theforce 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 was approximate. However for an

ideal gas the standardChapman-Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for anideal gas only undershock wave conditions.Boltzmann tried for many years to "prove" the

second law of thermodynamics using his gas-dynamical equation — his famousH-theorem . However the key assumption he made in formulating 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 overLoschmidt's paradox ultimately ended in his failure.Finally, in the 1970s E.G.D. Cohen and J.R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently nonequilibrium statistical mechanics for dense

gas es andliquid s focuses on theGreen-Kubo relations , thefluctuation theorem , and other approaches instead.**Energetics of evolution**Boltzmann's views played an essential role in the development of

energetics , the scientific study of energy flows under transformation. In 1922, for example,Alfred J. Lotka referred to Boltzmann as one of the first proponents of the proposition that available energy, also calledexergy , can be understood as the fundamental object under contention in the biological, or life-struggle and therefore also in the evolution of the organic world. [*Maximum power principle*] Lotka interpreted Boltzmann's view to imply that available energy could be the central concept that unified physics and biology as a quantitative physical principle of evolution. In the forward to Boltzmann's "Theoretical Physics and Philosophical Problems", S.R. de Groot noted thatHoward T. Odum later sought to develop these views when looking at the evolution of ecological systems, and suggested that themaximum power principle was an example of Darwin's law ofnatural selection .**ee also***

Boltzmann brain

*Boltzmann machine

*History of the molecule

*Lattice Boltzmann methods , a new method inComputational fluid dynamics which utilizes the theories of Boltzmann.

*Philosophy of thermal and statistical physics **References****Further reading*** Roman Sexl & John Blackmore (eds.), "Ludwig Boltzmann - Ausgewahlte Abhandlungen", (Ludwig Boltzmann Gesamtausgabe, Band 8), Vieweg, Braunschweig, 1982.

* John Blackmore (ed.), "Ludwig Boltzmann - His Later Life and Philosophy, 1900-1906, Book One: A Documentary History", Kluwer, 1995. ISBN 978-0-7923-3231-2

* John Blackmore, "Ludwig Boltzmann - His Later Life and Philosophy, 1900-1906, Book Two: The Philosopher", Kluwer, Dordrecht, Netherlands, 1995. ISBN 978-0-7923-3464-4

* John Blackmore (ed.), "Ludwig Boltzmann - Troubled Genius as Philosopher", in Synthese, Volume 119, Nos. 1 & 2, 1999, pp.1-232.

* Brush, Stephen G. (ed. & tr.), Boltzmann, "Lectures on Gas Theory", Berkeley, CA: U. of California Press, 1964

* Brush, Stephen G. (ed.), "Kinetic Theory", New York: Pergamon Press, 1965

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* Walter Hoeflechner (ed.), Ludwig Boltzmann - Leben und Briefe, Akademische Druck- u. Verlagsanstalt. Graz, Oesterreich, 1994

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* P. Ehrenfest & T. Ehrenfest (1911) "Begriffliche Grundlagen der statistischen Auffassung in der Mechanik", in: "Encyklopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen". Band IV, 2. Teil ( F. Klein and C. Müller (eds.). Leipzig: Teubner, pp. 3–90. Translated as "The conceptual Foundations of the Statistical Approach in Mechanics". New York: Cornell University Press, 1959. ISBN 0-486-49504-3

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* English translation by Morton Masius of the 2nd ed. of "Waermestrahlung". Reprinted by Dover (1959) & (1991). ISBN 0-486-66811-8

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* Reprinted: Dover (1979). ISBN 0-486-63896-0

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***External links*** Ruth Lewin Sime, "Lise Meitner: A Life in Physics" [

*http://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/lisemeitner.htm Chapter One: Girlhood in Vienna*] givesLise Meitner 's account of Boltzmann's teaching and career.

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* [*http://www.dieuniversitaet-online.at/beitraege/news/ludwig-boltzmann-leben-und-werk-zu-besichtigen/10.html Ludwig Boltzmann*] , Universität Wien (German).

* [*http://xxx.lanl.gov/abs/cond-mat/9608054 Boltzmann and Statistical Mechanics*] , by E.G.D. Cohen.

*Ali Eftekhari , [*http://philsci-archive.pitt.edu/archive/00001717/02/Ludwig_Boltzmann.pdf Ludwig Boltzmann (1844–1906)*] , manuscript that expands on Boltzmann's philosophical opinions and provides numerous quotes.

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*Persondata

NAME= Boltzmann, Ludwig

ALTERNATIVE NAMES=

SHORT DESCRIPTION=Austria nPhysicist

DATE OF BIRTH=February 20 ,1844

PLACE OF BIRTH=Vienna ,Austrian Empire

DATE OF DEATH=September 5 ,1906

PLACE OF DEATH=Duino ,Italy

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