title: Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble.
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.
authors.affiliation: Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.|Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
authors.forename: J L
authors.initials: JL
authors.lastname: Alonso
authors.affiliation: Fundación ARAID, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Castro
authors.affiliation: Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.|Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Clemente-Gallardo
authors.affiliation: Departament d'Enginyeria Agroforestal, Escola Tècnica Superior d'Enginyeria Agrària, Universitat de Lleida, Alcalde Rovira Roure 191, 25198 Lleida, Spain.
authors.forename: J C
authors.initials: JC
authors.lastname: Cuchí
authors.affiliation: Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.|Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.|Instituto de Química-Física Rocasolano, Consejo Superior de Investigaciones Científicas, Serrano 119, 28006 Madrid, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Echenique
authors.affiliation: Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
authors.forename: J G
authors.initials: JG
authors.lastname: Esteve
authors.affiliation: Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.|Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
authors.forename: F
authors.initials: F
authors.lastname: Falceto