Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-10-19
Physics
Condensed Matter
Statistical Mechanics
Revised version. Redundant assumption omitted. Microcanonical ensemble included. Reference added. 7 pages revtex
Scientific paper
10.1016/S0378-4371(01)00605-7
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 wavefunction). It has been stricktly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion-invariance, it is applicable to situations where persistent current occur. This clear-cut derivation allows to revive the ``no perpetuum mobile in equilibrium'' formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.
Allahverdyan Armen E.
Nieuwenhuizen Th. M.
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