Theory of entropy production in quantum many-body systems

Abstract

We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second and third laws of thermodynamics. For weakly-coupled subsystems of an isolated system, an expression for the long time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

“…Our numerical results for the entropy production and production rate corroborate and expand earlier studies [10][11][12][13][14]. These results also open a new route for determining the NE thermodynamical properties of quantum open systems under general conditions.…”

“…For example, the NE reduced density matrix in the central region ρ NE red,C is obtained from ρ NE red,α = Tr (L,R) [ρ NE ]. The corresponding entropy S NE C has been the object of recent studies [10][11][12][13][14], but it is clearly only a part of the entire entropy production in the system. For example, the contributions S NE L and S NE R are different from their (isolated) equilibrium counterparts S…”

“…The time dependence of the external force can be arbitrary or periodic [10,11,13,15]. The long-time limit behaviour of the NE thermodynamics also presents very interesting properties [12][13][14].…”

“…Originally the weak coupling limit of a finite-size central region interacting with thermal and/or particle baths was first considered [1, 2,[4][5][6]. Methods for dealing with the strong coupling limit have been recently developed [7][8][9][10][11][12][13][14]. 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.…”

Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators

“…More precisely one oscillator is in contact with a heat reservoir at a higher temperature and the other oscillator is in contact with a heat reservoir at a lower temperature. This arrangement allows us to calculate the thermal conductance [16][17][18][19] as well as the rate of the entropy production [18][19][20][21] and the atomic population [2], which are the main purpose of the present study. This calculation is achieved by the use of a quantum Fokker-Planck-Kramers (FPK) equation [19], understood as the canonical quantization of the ordinary FKP equation.…”