Ludwig Boltzmann
Ludwig Boltzmann Dr. habil. , 1869) | |
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Known for |
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Awards | ForMemRS (1899)[1] |
Scientific career | |
Fields | Physics |
Institutions |
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Thesis | Über die mechanische Bedeutung des zweiten Hauptsatzes der mechanischen Wärmetheorie (1866) |
Doctoral advisor | Josef Stefan |
Other academic advisors | |
Doctoral students | |
Other notable students | |
Signature | |
Ludwig Eduard Boltzmann (German pronunciation:
Statistical mechanics is one of the pillars of modern
Biography
Childhood and education
Boltzmann was born in Erdberg, a suburb of
Starting in 1863, Boltzmann studied
Academic career
In 1869 at age 25, thanks to a
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 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).[8] Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst.[9][10] He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.
Boltzmann was appointed to the Chair of Theoretical Physics at the
In 1894, Boltzmann succeeded his teacher
Final years and death
Boltzmann spent a great deal of effort in his final years defending his theories.
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 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[when?] at the Palace.[13]
In 1905, he gave an invited course of lectures in the summer session at the
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.[11][15] 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).[16][17][18][15] He is buried in the Viennese
Philosophy
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 the physical chemist Wilhelm Ostwald disbelieved their existence.[19] 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.[20]
Boltzmann wrote treatises on philosophy such as "On the question of the objective existence of processes in inanimate nature" (1897). He was a realist.[21] 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."[22]
Physics
Boltzmann's most important scientific contributions were in 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 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.[23] It was Boltzmann who derived the first equation to model the dynamic evolution of the probability distribution Maxwell and he had created.[24] 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 is contributed to by heat, spatial separation, and radiation.[25] 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.
To quote
where kB is the
where i ranges over all possible molecular conditions, and where denotes
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.[30]
Boltzmann equation
The Boltzmann equation was developed to describe the dynamics of an ideal gas.
where ƒ 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. (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
The form of the collision term assumed by Boltzmann 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 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
Second thermodynamics law as a law of disorder
The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") 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,[31] Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at 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).[32] The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are 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, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."[33]
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
Ludwig Boltzmann's legacy and impact on modern science
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 the foundation for some of the most fundamental concepts in physics. For instance,
Atomic theory and the existence of atoms and molecules
Boltzmann's kinetic theory of gases was one of the first attempts to explain macroscopic properties, such as pressure and temperature, in terms of the behavior 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 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 and the Boltzmann constant
Statistical mechanics, which Boltzmann pioneered, connects macroscopic observations with microscopic behaviors. His statistical explanation of the second law of thermodynamics was a significant achievement, and he provided the current definition of entropy (), where kB is the Boltzmann constant and Ω is the number of microstates corresponding to a given macrostate.
Max Planck later named the constant kB as 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.
The Boltzmann Equation and Modern Uses
Because the
Influence on quantum mechanics
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 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.[40] One biographer of Boltzmann says that Boltzmann’s approach “pav[ed] the way for Planck.”[41]
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 the quantization of energy levels had a profound influence on the development of quantum physics.
Works
- Verhältniss zur Fernwirkungstheorie, Specielle Fälle der Elektrostatik, stationären Strömung und Induction (in German). Vol. 2. Leipzig: Johann Ambrosius Barth. 1893.
- Theorie van der Waals, Gase mit zusammengesetzten Molekülen, Gasdissociation, Schlussbemerkungen (in German). Vol. 2. Leipzig: Johann Ambrosius Barth. 1896.
- Theorie der Gase mit einatomigen Molekülen, deren Dimensionen gegen die mittlere Weglänge verschwinden (in German). Vol. 1. Leipzig: Johann Ambrosius Barth. 1896.
- Abteilung der Grundgleichungen für ruhende, homogene, isotrope Körper (in German). Vol. 1. Leipzig: Johann Ambrosius Barth. 1908.
- Vorlesungen über Gastheorie (in French). Paris: Gauthier-Villars. 1922.
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Volumes I and II of Vorlesungen über Gastheorie (1896-1898)
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Title page to volumes I and II of Vorlesungen über Gastheorie (1896-1898)
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Table of contents to volumes I and II of Vorlesungen über Gastheorie (1896-1898)
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Introduction to volumes I and II of Vorlesungen über Gastheorie (1896-1898)
Awards and honours
In 1885 he became a member of the Imperial
See also
- Thermodynamics
- Statistical Mechanics
References
- ^ a b "Fellows of the Royal Society". London: Royal Society. Archived from the original on 16 March 2015.
- ISBN 0-85229-135-3.
- Partington, J.R. (1949), An Advanced Treatise on Physical Chemistry, vol. 1, Fundamental Principles, The Properties of Gases, London: Longmans, Green and Co., p. 300
- ^ Gibbs, Josiah Willard (1902). Elementary Principles in Statistical Mechanics. New York: Charles Scribner's Sons.
- ISBN 978-0-8065-3678-1.
- ^ ISBN 978-0-521-01706-0.
- ^ Južnič, Stanislav (December 2001). "Ludwig Boltzmann in prva študentka fizike in matematike slovenskega rodu" [Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent]. Kvarkadabra (in Slovenian) (12). Retrieved 17 February 2012.
- ^ "Ludwig Boltzmann biography (20 Feb 1844 – 5 Sept 1906)".[full citation needed]
- S2CID 30499879.
Paul Ehrenfest (1880–1933) along with Nernst, Arrhenius, and Meitner must be considered among Boltzmann's most outstanding students.
- ^ "Walther Hermann Nernst". Archived from the original on 12 June 2008.
Walther Hermann Nernst visited lectures by Ludwig Boltzmann
- ^ ISBN 978-0-19-850154-1
- .
- ^ The Boltzmann Equation: Theory and Applications, E. G. D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012
- ISSN 0031-9228.
- ^ a b Nina Bausek and Stefan Washietl (13 February 2018). "Tragic deaths in science: Ludwig Boltzmann – a mind in disorder". Paperpile. Retrieved 26 April 2020.
- ISBN 1-78087-325-5
- ISBN 978-0-7923-3464-4.
- ^ Upon Boltzmann's death, Friedrich ("Fritz") Hasenöhrl became his successor in the professorial chair of physics at Vienna.
- ISBN 978-0-316-10930-7.
- ]
- ]
- ISBN 978-0-19-850154-1.
- ^ Ludwig Boltzmann, Lectures on the Theory of Gases, translated by Stephen G. Brush, "Translator's Introduction", 1968.
- ISBN 978-0198570646.
- ^ Max Planck, p. 119.
- ^ The concept of entropy was introduced by Rudolf Clausius in 1865. He was the first to enunciate the second law of thermodynamics by saying that "entropy always increases".
- ^ "A Mathematical Theory of Communication by Claude E. Shannon". cm.bell-labs.com. Archived from the original on 3 May 2007.
- ISBN 978-0-262-66035-8., p. 21
- .
- ^ Maxwell, J. (1871). Theory of heat. London: Longmans, Green & Co.
- ^ Boltzmann, L. (1974). The second law of thermodynamics. Populare Schriften, Essay 3, address to a formal meeting of the Imperial Academy of Science, 29 May 1886, reprinted in Ludwig Boltzmann, Theoretical physics and philosophical problem, S. G. Brush (Trans.). Boston: Reidel. (Original work published 1886)
- ^ Boltzmann, L. (1974). The second law of thermodynamics. p. 20
- ^ "Collier's Encyclopedia", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15
- ^ "Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275
- ^ A. Douglas Stone, “Einstein and the Quantum “, Chapter 1 “An Act of Desperation.” 2015.
- ^ Advanced Theory of Semiconductors and Semiconductor Devices Numerical Methods and Simulation / Umberto Ravaioli http://transport.ece.illinois.edu/ECE539S12-Lectures/Chapter2-DriftDiffusionModels.pdf
- ^ AN OVERVIEW OF THE BOLTZMANN TRANSPORT EQUATION SOLUTION FOR NEUTRONS, PHOTONS AND ELECTRONS IN CARTESIAN GEOMETRY,
Ba ́rbara D. do Amaral Rodriguez, Marco Tu ́llio Vilhena, 2009 International Nuclear Atlantic Conference - INAC 2009 Rio de Janeiro, RJ, Brazil, September 27 to October 2, 2009 ASSOCIAC ̧A ̃OBRASILEIRADEENERGIANUCLEAR-ABEN ISBN 978-85-99141-03-8
- ^ Sharp, K.; Matschinsky, F. Translation of Ludwig Boltzmann’s Paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium” Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp 373-435 (Wien. Ber. 1877, 76:373-435). Reprinted in Wiss. Abhandlungen, Vol. II, reprint 42, p. 164-223, Barth, Leipzig, 1909. Entropy 2015, 17, 1971-2009. https://doi.org/10.3390/e17041971 https://www.mdpi.com/1099-4300/17/4/1971
- ISBN 978-0198570646.
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.
- Blundell, Stephen; Blundell, Katherine M. (2006). Concepts in Thermal Physics. Oxford University Press. p. 29. ISBN 978-0-19-856769-1.
- Boltzmann, Ludwig Boltzmann – Leben und Briefe, ed., Walter Hoeflechner, Akademische Druck- u. Verlagsanstalt. Graz, Oesterreich, 1994
- Brush, Stephen G. (ed. & tr.), Boltzmann, Lectures on Gas Theory, Berkeley, California: U. of California Press, 1964
- Brush, Stephen G. (ed.), Kinetic Theory, New York: Pergamon Press, 1965
- Brush, Stephen G. (1970). "Boltzmann". In Charles Coulston Gillispie (ed.). Dictionary of Scientific Biography. New York: Scribner. ISBN 978-0-684-16962-0.
- Brush, Stephen G. (1986). The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases. Amsterdam: North-Holland. ISBN 978-0-7204-0370-1.
- ISBN 978-0-19-850154-1.
- Darrigol, Olivier (2018). Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical. ISBN 978-0-19-881617-1.
- ISBN 0-486-49504-3
- Everdell, William R (1988). "The Problem of Continuity and the Origins of Modernism: 1870–1913". History of European Ideas. 9 (5): 531–552. .
- Everdell, William R (1997). The First Moderns. Chicago: University of Chicago Press. ISBN 9780226224800.
- Gibbs, Josiah Willard (1902). Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics. New York: Charles Scribner's Sons.
- Johnson, Eric (2018). Anxiety and the Equation: Understanding Boltzmann's Entropy. The MIT Press. ISBN 978-0-262-03861-4.
- Klein, Martin J. (1973). "The Development of Boltzmann's Statistical Ideas". In ISBN 978-0-387-81137-6.
- ISBN 978-0-684-85186-0.
- Lotka, A. J. (1922). "Contribution to the Energetics of Evolution". Proc. Natl. Acad. Sci. U.S.A. 8 (6): 147–51. PMID 16576642.
- Meyer, Stefan (1904). Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage 20. Februar 1904 (in German). J. A. Barth.
- ISBN 0-486-66811-8
- Sharp, Kim (2019). Entropy and the Tao of Counting: A Brief Introduction to Statistical Mechanics and the Second Law of Thermodynamics (SpringerBriefs in Physics). Springer Nature. ISBN 978-3030354596
- Tolman, Richard C. (1938). The Principles of Statistical Mechanics. Oxford University Press. Reprinted: Dover (1979). ISBN 0-486-63896-0
External links
- Uffink, Jos (2004). "Boltzmann's Work in Statistical Physics". Stanford Encyclopedia of Philosophy. Retrieved 11 June 2007.
- O'Connor, John J.; Robertson, Edmund F., "Ludwig Boltzmann", MacTutor History of Mathematics Archive, University of St Andrews
- Ruth Lewin Sime, Lise Meitner: A Life in Physics Chapter One: Girlhood in Vienna gives Lise Meitner's account of Boltzmann's teaching and career.
- Eftekhari, Ali, "Ludwig Boltzmann (1844–1906)." Discusses Boltzmann's philosophical opinions, with numerous quotes.
- Rajasekar, S.; Athavan, N. (7 September 2006). "Ludwig Edward Boltzmann". arXiv:physics/0609047.
- Ludwig Boltzmann at the Mathematics Genealogy Project
- ScienceWorld.