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The physics and mathematics of the second law of thermodynamics

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Lieb, Elliott H., Yngvason, Jakob·1999·Physics Reports
DOI 10.1016/s0370-1573(98)00082-9
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Abstract

The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of `hotness' is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.

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Metadata

Authors
Lieb, E. H., & Yngvason, J.
Venue
Physics Reports
Publisher
Elsevier BV
Published
1999-03
Volume
310
Issue
1
Pages
1-96
ISSN
0370-1573 (ISSN-L)
DOI
10.1016/s0370-1573(98)00082-9
OpenAlex
W2154803134
Cited by
532
References
0
FWCI
9.35
Type
journal article
Language
en
Open access
green

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CoChat. (2026). Citation check: The physics and mathematics of the second law of thermodynamics. https://app.cochat.ai/papers/10.1016/s0370-1573(98)00082-9
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Lieb, E. H., & Yngvason, J. (1999). The physics and mathematics of the second law of thermodynamics. Physics Reports. https://doi.org/10.1016/s0370-1573(98)00082-9

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.