期刊
STUDIES IN HISTORY AND PHILOSOPHY OF MODERN PHYSICS
卷 36B, 期 2, 页码 275-290出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.shpsb.2005.01.001
关键词
heat theorem; equipartition; ergodic theory; micro-canonical; metric indecomposability; adiabatic invariance; volume entropy
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). (c) 2005 Elsevier Ltd. All rights reserved.
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