# Entropy production as correlation between system and reservoir

@article{Esposito2010EntropyPA, title={Entropy production as correlation between system and reservoir}, author={Massimiliano Esposito and Katja Lindenberg and Christian Van den Broeck}, journal={New Journal of Physics}, year={2010}, volume={12}, pages={013013} }

We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs, each of which is initially described by a canonical equilibrium distribution. Although the total entropy of system plus reservoirs is conserved, we show that system entropy production is always positive and is a direct measure of system–reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our…

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## References

SHOWING 1-10 OF 40 REFERENCES

Entropy production along a stochastic trajectory and an integral fluctuation theorem.

- PhysicsPhysical review letters
- 2005

The integrated sum of both Delatas(tot) is shown to obey a fluctuation theorem (exp([-Deltas( tot) = 1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval)).

Entropy production and the arrow of time

- Physics
- 2009

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states.…

Entropy production and time asymmetry in nonequilibrium fluctuations.

- PhysicsPhysical review letters
- 2007

Experimental results are presented showing that the difference of a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current equals the thermodynamic entropy production in units of Boltzmann's constant.

Fluctuation theorem for arbitrary open quantum systems.

- PhysicsPhysical review letters
- 2009

The validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems because the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between thefree energy of the total system and that of the bare environment.

Dissipation: the phase-space perspective.

- PhysicsPhysical review letters
- 2007

It is shown that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by =W-DeltaF=kTD(rho||rho[ over ])=kT, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process.

Quantum signatures of chaos

- Physics
- 1991

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,…

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

- Computer Science
- 2004

The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.

Erratum: Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

- Computer Science
- 2004

The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.

Nonequilibrium work theorem for a system strongly coupled to a thermal environment

- Physics
- 2004

In a recent paper (2004 J. Stat. Mech.: Theor. Exp. P07006), Cohen and Mauzerall (CM) have argued that the derivation of the nonequilibrium work relation given in a previous work of Jarzynski (1997…

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

- PhysicsPhysical review letters
- 1995

This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.