Abstract
We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both a temperature and a chemical potential differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs-von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.
Highlights
The understanding of irreversible phenomena is a long-standing problem in statistical mechanics.Explanations of the fundamental laws of phenomenological nonequilibrium (NE) thermodynamics have been given and applied to quantum open systems for several decades [1,2]
We have shown that the NE steady state can be considered as a pseudo equilibrium state with a corresponding density matrix which is given in the form of a generalised Gibbs ensemble
We have shown that the NE steady state can be considered as a pseudo equilibrium state with a corresponding generalised Gibbs ensemble given by ρNE
Summary
The understanding of irreversible phenomena is a long-standing problem in statistical mechanics. One can study the NE thermodynamical properties and the entropy production in such systems when an external driving force is applied to the central region. After some time much longer than some typical relaxation times of the finite system, a steady state can be obtained Such a state arises from the balance between irreversible processes (fluxes of particle and/or energy) and the driving forces induced by the reservoirs. It opens a new route to the calculations of the full NE response functions of the system, such as the NE charge susceptibility [22] or the NE specific heat of the central region
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