Thermodynamic fluctuation relation for temperature and energy

Details Thermodynamic fluctuation relation for temperature and energy Thermodynamic fluctuation relation for temperature and energy

2007-02-01

arxiv.org/abs/cond-mat/0702031v2

J. Phys. A: Math and Theo. 42, 095006 2009

Physics

Condensed Matter

Statistical Mechanics

Version accepted for publication in J. Phys. A: Math and Theo

Scientific paper

10.1088/1751-8113/42/9/095006

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $< \delta \beta \delta {E}> =1+< \delta {E^{2}}% > \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.

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