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Article ID: CBB000771640

On the Mechanical Foundations of Thermodynamics: The Generalized Helmholtz Theorem (2005)

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Volume: 36
Pages: 275--290

Publication Date: 2005
Edition Details: Part of a special issue: “Philosophical and Foundational Issues in Statistical Physics”
Language: English

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Statistical mechanics Physics Thermodynamics 19th century Helmholtz, Hermann Ludwig Ferdinand von Boltzmann, Ludwig

An elegant but seldom appreciated effort to provide a mechanical model of equilibrium thermodynamics dates back to the Helmholtz theorem (HT). According to this theorem, the thermodynamic relations hold mechanically (without probabilistic assumptions) in the case of one-dimensional monocyclic systems. Thanks to a discrete picture of the phase space, Boltzmann was able to apply the HT to multi-dimensional ergodic systems, suggesting that the thermodynamic relations we observe in macroscopic systems at equilibrium are a direct consequence of the microscopic laws of dynamics alone. Here I review Boltzmann's argument and show that, using the language of the modern ergodic theory, it can be safely re-expressed on a continuum phase space as a generalized Helmholtz theorem (GHT), which can be readily proved. Along the way the agreement between the Helmholtz--Boltzmann theory and that of P. Hertz (based on adiabatic invariance) is revealed. Both theories, in fact, lead to define the entropy as the logarithm of the phase-space volume enclosed by the constant energy hyper-surface (volume entropy).

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Description A review of Boltzmann's argument on the Helmholtz theorem.

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Article Uffink, Jos (2005) Introduction. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics (p. 219). unapi

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https://data.isiscb.org/isis/citation/CBB000771640/

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