Thermodynamic fluctuation relation for temperature and energy

Abstract

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 $<\delta \beta \delta E>=1+<\delta E^2$ 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.

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

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• Extending canonical Monte Carlo methods
• Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions
• Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique
• Extending canonical Monte Carlo methods II
• Fluctuations of intensive quantities in statistical thermodynamics
• Conditional maximum entropy and Superstatistics
• Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem
• Thermodynamic origin of quantum time-energy uncertainty relation