Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

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.

published in Entropy 19, 158 (2007)

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• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
• Quantum battery charging by non-equilibrium steady-state currents
• Corrections to the Hamiltonian induced by finite-strength coupling to the environment
• Relating Heat and Entanglement in Strong Coupling Thermodynamics
• Transport and thermodynamics in quantum junctions: A scattering approach
• Exact steady state of perturbed open quantum systems
• Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: Non-equilibrium entropy production and higher order corrections