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A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

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  • Allahverdyan, A.E.
  • Nieuwenhuizen, Th.M.

Abstract

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (“cyclic changes cost energy”), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wave function). It has been strictly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble.

Suggested Citation

  • Allahverdyan, A.E. & Nieuwenhuizen, Th.M., 2002. "A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 542-552.
    • Handle: RePEc:eee:phsmap:v:305:y:2002:i:3:p:542-552
    DOI: 10.1016/S0378-4371(01)00605-7
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    Cited by:

    1. Seifert, Udo, 2020. "Entropy and the second law for driven, or quenched, thermally isolated systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).

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