# Duality and hidden equilibrium in transport models

@article{Frassek2020DualityAH, title={Duality and hidden equilibrium in transport models}, author={Rouven Frassek and Cristian Giardin{\`a} and Jorge Kurchan}, journal={arXiv: Statistical Mechanics}, year={2020} }

A large family of diffusive models of transport that has been considered in the past years admits a transformation into the same model in contact with an equilibrium bath. This mapping holds at the full dynamical level, and is independent of dimension or topology. It provides a good opportunity to discuss questions of time reversal in out of equilibrium contexts. In particular, thanks to the mapping one may define the free-energy in the non-equilibrium states very naturally as the (usual) free…

## Figures from this paper

## 6 Citations

Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains

- Mathematics
- 2021

We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish:…

Steady state large deviations for one-dimensional, symmetric exclusion processes in weak contact with reservoirs

- Mathematics
- 2021

Consider the symmetric exclusion process evolving on an interval and weakly interacting at the end-points with reservoirs. Denote by I[0,T ](·) its dynamical large deviations functional and by V (·)…

Exact solution of an integrable non-equilibrium particle system

- Mathematics
- 2021

We consider the boundary-driven interacting particle systems introduced in [FGK20a] related to the open non-compact Heisenberg model in one dimension. We show that a finite chain of N sites connected…

Entanglement distribution in the quantum symmetric simple exclusion process.

- PhysicsPhysical review. E
- 2021

The probability distribution of entanglement in the quantum symmetric simple exclusion process, a model of fermions hopping with random Brownian amplitudes between neighboring sites, is studied by means of a Coulomb gas approach from random matrix theory and analytically the large-deviation function of the entropy in the thermodynamic limit is computed.

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

- Physics
- 2020

Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant…

Duality in quantum transport models

- Physics
- 2020

We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a…

## References

SHOWING 1-10 OF 74 REFERENCES

Duality for Stochastic Models of Transport

- Mathematics
- 2013

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model…

Duality and Hidden Symmetries in Interacting Particle Systems

- Mathematics
- 2009

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in…

Duality and exact correlations for a model of heat conduction

- Physics
- 2007

We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the…

Mapping out-of-equilibrium into equilibrium in one-dimensional transport models

- Physics
- 2008

Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out-of-equilibrium systems. The evolution…

Exact Solution to Integrable Open Multi-species SSEP and Macroscopic Fluctuation Theory

- Mathematics
- 2016

We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant…

Macroscopic fluctuation theory

- Physics
- 2015

Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new…

Fourier’s Law for a Microscopic Model of Heat Conduction

- Physics
- 2005

We consider a chain of N harmonic oscillators perturbed by a conservative stochastic dynamics and coupled at the boundaries to two gaussian thermostats at different temperatures. The stochastic…

Free energy functional for nonequilibrium systems: an exactly solvable case.

- PhysicsPhysical review letters
- 2001

This work considers the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials and yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

Heat flow in an exactly solvable model

- Physics
- 1982

A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy…

Entropy of Open Lattice Systems

- Computer Science
- 2007

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in…