Probabilities and statistical mechanics of large and small systems

Domagoj Kuić
Faculty of Science, University of Split,

It is known that statistical mechanics reproduces the thermodynamic properties of large systems in equilibrium. Standard examples are thermodynamic potentials derived in statistical mechanics for systems described by microcanonical, canonical or grand canonical ensemble. However, use of these ensembles is generally based on the assumption that the interaction of the system with its environment is weak, and therefore, the correlations existing between the degrees of freedom of the two can be neglected. This effectively means the statistical independence of the system and environment microscopic degrees of freedom. On the other hand, for „very small“ systems driven out of thermodynamic equilibrium by external forcing, the assumption of weak interaction between the system and its environment compared to the bare system Hamiltonian is not always justified. By following the approach of [1], which extends the validity of the Crooks fluctuation theorem [2] and the Jarzynski nonequilibrium work relation [3] to the quantum systems strongly coupled with their environments, we explain how that leads to a reformulation of the standard statistical mechanics expressions for thermodynamic quantities like free energy and entropy. This raises also interesting questions about the additivity and extensivity of these quantities.

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[1] M. Campisi, P. Talkner, P. Hanggi, Phys. Rev. Lett. 102, 210401 (2009)
[2] G.E. Crooks, Phys. Rev. E 60, 2721 (1999)
[3] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)
[4] D. Kuić, Eur. Phys. J. B 89,124 (2016)