Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J L AlonsoF Falceto

Abstract

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions and prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea cannot be used to construct an appropriate quantum equilibrium thermodynamics.

References

Dec 24, 2009·The Journal of Physical Chemistry. a·Barbara Fresch, Giorgio J Moro
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Boris V Fine
Jul 24, 2010·The Journal of Chemical Physics·Barbara Fresch, Giorgio J Moro
Mar 17, 2011·Physical Review Letters·Sang Wook KimMasahito Ueda
Aug 27, 2011·Physical Review Letters·Kai Ji, Boris V Fine
Aug 17, 2012·The Journal of Chemical Physics·J L AlonsoF Falceto
Nov 19, 2013·Physical Review Letters·Martin PleschVlatko Vedral
Nov 19, 2013·Physical Review Letters·Sang Wook KimMasahito Ueda

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Citations

Nov 21, 2020·Physical Review. E·J L AlonsoJ A Jover-Galtier

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