Wigner entropy production and heat transport in linear quantum lattices

Abstract

When a quantum system is coupled to several heat baths at different temperatures, it eventually reaches a non-equilibrium steady state featuring stationary internal heat currents. These currents imply that entropy is continually being produced in the system at a constant rate. In this paper we apply phase-space techniques to the calculation of the Wigner entropy production on general linear networks of harmonic nodes. Working in the ubiquitous limit of weak internal coupling and weak dissipation, we obtain simple closed-form expressions for the entropic contribution of each individual quasi-probability current. Our analysis highlights the essential role played by the internal unitary interactions (node-node couplings) in maintaining a non-equilibrium steadystate and hence a finite entropy production rate. We also apply this formalism to the paradigmatic problem of energy transfer through a chain of oscillators subject to self-consistent internal baths that can be used to tune the transport from ballistic to diffusive. We find that the entropy production scales with different power law behaviors in the ballistic and diffusive regimes, hence allowing us to quantify what is the "entropic cost of diffusivity." *

Analysis of the conditional mutual information in ballistic and diffusive non-equilibrium steady-states

“…Additional discussions on the use of Gaussian techniques to solve this model can also be found in Ref. [61].…”

Irreversible Entropy Production rate in a parametrically driven-dissipative System: The Role of Self-Correlation between Noncommuting Observables

“…More recently, considerable attention has been directed towards the theoretical and experimental characterization of entropy production in non-equilibrium bosonic systems based on the quantum phase space distributions and Fokker-Planck equations [18][19][20][21][22][23][24][25][26][27][28].…”

“…In this framework, one can express entropy production in terms of means and variances of independent variables and identify irreversible quasi-probability currents in phase space for single-mode Gaussian systems in contact to a sin-gle reservoir [19,22] and multi-mode Gaussian systems connected to multiple reservoirs [18,23,24,28]. Identifying the quasi-probability currents in phase space provides physical interpretations for the irreversibility in the microscopic systems at the quantum level [22].…”

“…Identifying the quasi-probability currents in phase space provides physical interpretations for the irreversibility in the microscopic systems at the quantum level [22]. It can keep Wigner entropy production rate finite for a system in contact with a thermal reservoir at zero temperature [21,23]. Also, the formalism works very well to describe irreversibility in open quantum systems exposed to different non-equilibrium reservoirs such as squeezed and dephasing reservoirs [19].…”

Entropy production and Onsager reciprocal relations describing the relaxation to equilibrium in stochastic thermodynamics

“…[74], where the authors considered the structure of the McLennan steady nonequilibrium ensemble [75]. These approaches have been generalized to the study of linear quantum systems as well [76,77]. Also the study of the entropy production for non-Markovian dynamical systems has been recently addressed [78,79].…”