- Ludwig Boltzmann
name = Ludwig Boltzmann
image_width = 225px
caption = Ludwig Eduard Boltzmann (1844-1906)
birth_date = birth date|1844|2|20|mf=y
Vienna, Austrian Empire
death_date = death date and age|1906|9|5|1844|2|20|mf=y
Duinonear Trieste, Italy(at that time Austrian Empire)
University of Graz University of Vienna University of Munich University of Leipzig
University of Vienna
Paul Ehrenfest Philipp Frank Gustav Herglotz Lise Meitner
Boltzmann's constant Boltzmann equation H-theorem Boltzmann distribution Stefan-Boltzmann law
Ludwig Eduard Boltzmann (
February 20, 1844– September 5, 1906) was an Austrian physicistfamous for his founding contributions in the fields of statistical mechanicsand statistical thermodynamics. He was one of the most important advocates for atomic theorywhen that scientific model was still highly controversial.
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 from Berlin, was a clock manufacturer, and Boltzmann’s mother, Katharina Pauernfeind, was originally from Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. At age 15, Boltzmann lost his father.
physicsat the University of Vienna, starting in 1863. Among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausenand 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 a Privatdozent(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.
In 1869, at age 25, he was appointed full Professor of Mathematical Physics at the
University of Grazin the province of Styria. In 1869 he spent several months in Heidelbergworking with Robert Bunsenand Leo Königsbergerand then in 1871 he was with Gustav Kirchhoffand Hermann von Helmholtzin Berlin. In 1873 Boltzmann joined the University of Viennaas 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. On July 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 were Svante Arrheniusand Walther 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
last2 = Nabl
first2 = Josef
last3 = Meyer
first3 = Stephan
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
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
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 Imperial
Austrian Academy of Sciencesand in 1887 he became the President of the University of Graz.
Boltzmann was appointed to the Chair of Theoretical Physics at the
University of Munichin Bavaria, Germany in 1890.In 1893, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.
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 the University of Leipzig, on the invitation of Wilhelm Ostwald. After the retirement of Mach due to bad health, Boltzmann came back to Vienna in 1902. His students included Karl Przibram, Paul Ehrenfestand Lise 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 between Mardi Grasand Ash 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.
September 5, 1906, while on a summer vacation in Duino, near Trieste, Boltzmann hanged himself during an attack of depression. He is buried in the Viennese Zentralfriedhof; his tombstone bears the inscription S=k. 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 Machand the physical chemist Wilhelm Ostwaldopposed 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 of Lamarck'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 philosopher Franz Brentanoin 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.
Boltzmann's most important scientific contributions were in
kinetic theory, including the Maxwell-Boltzmann distributionfor molecular speeds in a gas. In addition, Maxwell-Boltzmann statisticsand the Boltzmann distributionover 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
physicsestablishment did not share his belief in the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotlandand Gibbs in the United States; and by most chemists since the discoveries of John Daltonin 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 of colloidal suspensions (1908-1909) confirmed the values of Avogadro's numberand Boltzmann's constant, and convinced the world that the tiny particles really exist.
To quote Planck, "The
logarithmic connection between entropyand probabilitywas first stated by L. Boltzmann in his kinetic theoryof gases" [Max Planck, p. 119.] This famous formula for entropy is [The concept of entropywas introduced by Rudolf Clausiusin 1865. He was the first to enunciate the second law of thermodynamicsby 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 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).]
where = 1.3806505(24) × 10−23 J K−1 is Boltzmann's constant, and the
logarithmis taken to the natural base . is the "Wahrscheinlichkeit", the frequency of occurrence of a macrostate[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 an ideal gasof "identical" particles, of which are in the -th microscopic condition (range) of position and momentum. can be counted using the formula for permutations
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. is called the " thermodynamic probability" since it is an integergreater than one, while mathematical probabilities are always numbers between zero and one.
The equation for 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
where represents the distribution function of single-particle position and momentum at a given time (see the
Maxwell-Boltzmann distribution), is a force, is the mass of a particle, is the time and 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 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 equationhas a deceptively simple appearance, since can represent an arbitrary single-particle distribution function. Also, the forceacting on the particles depends directly on the velocity distribution function "f". The Boltzmann equation is notoriously difficult to integrate. David Hilbertspent years trying to solve it without any real success.
The form of the collision term assumed by Boltzmann was approximate. However for an
ideal gasthe standard Chapman-Enskogsolution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gasonly under shock waveconditions.
Boltzmann tried for many years to "prove" the
second law of thermodynamicsusing his gas-dynamical equation — his famous H-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 over Loschmidt's paradoxultimately 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
gases and liquids focuses on the Green-Kubo relations, the fluctuation 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. Lotkareferred to Boltzmann as one of the first proponents of the proposition that available energy, also called exergy, 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 that Howard T. Odumlater sought to develop these views when looking at the evolution of ecological systems, and suggested that the maximum power principlewas an example of Darwin's law of natural selection.
History of the molecule
Lattice Boltzmann methods, a new method in Computational fluid dynamicswhich utilizes the theories of Boltzmann.
Philosophy of thermal and statistical physics
* 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
* Walter Hoeflechner (ed.), Ludwig Boltzmann - Leben und Briefe, Akademische Druck- u. Verlagsanstalt. Graz, Oesterreich, 1994
* 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
* English translation by Morton Masius of the 2nd ed. of "Waermestrahlung". Reprinted by Dover (1959) & (1991). ISBN 0-486-66811-8
* Reprinted: Dover (1979). ISBN 0-486-63896-0
* 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] gives
Lise Meitner's account of Boltzmann's teaching and career.
* [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.
NAME= Boltzmann, Ludwig
DATE OF BIRTH=
February 20, 1844
PLACE OF BIRTH=
Vienna, Austrian Empire
DATE OF DEATH=
September 5, 1906
PLACE OF DEATH=
Wikimedia Foundation. 2010.
Look at other dictionaries:
Ludwig Boltzmann — Naissance 20 février 1844 Vienne ( … Wikipédia en Français
Ludwig Boltzmann — Ludwig Boltzmann. Ludwig Edward Boltzmann (Viena, 20 de febrero de 1844 Duino, Italia, 5 de septiembre de 1906) fue un físico austriaco pionero de la mecánica estadística, autor de la llamada constante de Boltzm … Wikipedia Español
Ludwig Boltzmann — Boltzmanns Bild in der Dibner Kollektion … Deutsch Wikipedia
Ludwig Boltzmann — Ludwig Edward Boltzmann (Viena, 1844 Duino, Italia, 1906) Físico austriaco. Estudió en la Universidad de Viena, por la que recibió su doctorado en 1866. Fue profesor de física y matemáticas en Viena, Graz, Munich y Leipzig. Boltzmann contribuyó… … Enciclopedia Universal
Ludwig Boltzmann — noun Austrian physicist who contributed to the kinetic theory of gases (1844 1906) • Syn: ↑Boltzmann • Instance Hypernyms: ↑physicist … Useful english dictionary
Ludwig Boltzmann Gesellschaft — Die Ludwig Boltzmann Gesellschaft (LBG), benannt nach dem österreichischen Physiker Ludwig Boltzmann, ist eine österreichische Trägerorganisation für außeruniversitäre Forschung im Bereich Medizin, Geistes , Sozial und Kulturwissenschaften und… … Deutsch Wikipedia
Ludwig-Boltzmann-Institut — Die Ludwig Boltzmann Gesellschaft ist eine österreichische Gesellschaft zur Förderung der Grundlagenforschung und der angewandten Forschung im medizinischen, geistes , sozial und kulturwissenschaftlichen Bereich. Sie wurde 1961 gegründet und… … Deutsch Wikipedia
Ludwig Boltzmann Institut für Menschenrechte — Das Ludwig Boltzmann Institut für Menschenrechte (BIM) ist eine außeruniversitäre Forschungseinrichtung der Ludwig Boltzmann Gesellschaft (LBG) und sieht sich der Forschung und Lehre auf dem Gebiet der Menschenrechte verpflichtet. Das BIM wurde… … Deutsch Wikipedia
Ludwig-Boltzmann-Preis — Als Ludwig Boltzmann Preise werden zwei österreichische Auszeichnungen bezeichnet, und zwar: der Ludwig Boltzmann Preis (ÖPG), ein Nachwuchspreis der Österreichisch physikalischen Gesellschaft der Ludwig Boltzmann Staatspreis für… … Deutsch Wikipedia
Ludwig-Boltzmann-Preis (ÖPG) — Der Ludwig Boltzmann Preis wird alle zwei Jahre von der Österreichischen Physikalischen Gesellschaft für hervorragende Leistungen auf dem Gebiet der theoretischen Physik vergeben. Er ist nach Ludwig Boltzmann benannt. Gestiftet wurde der Ludwig… … Deutsch Wikipedia