# Wigner entropy production and heat transport in linear quantum lattices

@article{Malouf2019WignerEP, title={Wigner entropy production and heat transport in linear quantum lattices}, author={William T. B. Malouf and Jader P. Santos and Luis A. Correa and Mauro Paternostro and Gabriel T. Landi}, journal={Physical Review A}, year={2019} }

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…

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## References

SHOWING 1-10 OF 69 REFERENCES

Heat Transport in Harmonic Lattices

- Physics
- 2006

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic…

Microscopic theory of a nonequilibrium open bosonic chain.

- PhysicsPhysical review. E
- 2016

This paper shows how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials, and finds that they have the structure of Landauer's formula.

Entropy production in nonequilibrium systems at stationary states.

- PhysicsPhysical review letters
- 2012

A stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation is presented, finding a singularity at the critical point of the linear-logarithm type.

Non-additive dissipation in open quantum networks out of equilibrium

- Physics
- 2017

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of…

The thermodynamic cost of driving quantum systems by their boundaries

- PhysicsScientific reports
- 2015

This work considers systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation, and shows that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.

Properties of a Harmonic Crystal in a Stationary Nonequilibrium State

- Physics
- 1967

The stationary nonequilibrium Gibbsian ensemble representing a harmonic crystal in contact with several idealized heat reservoirs at different temperatures is shown to have a Gaussian r space…

Stochastic thermodynamics, fluctuation theorems and molecular machines.

- PhysicsReports on progress in physics. Physical Society
- 2012

Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Thermal transport in out-of-equilibrium quantum harmonic chains.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction are assessed and how such a possibility depends on the environment linked to the system are highlighted.

Entropy production in irreversible systems described by a Fokker-Planck equation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

The irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation and the connection between the definition of entropy production rate and the Jarzynski equality is shown.

Fourier's Law for a Harmonic Crystal with Self-Consistent Stochastic Reservoirs

- Physics
- 2004

We consider a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site. The temperatures of the “exterior” left and right heat baths are at specified values…