Duality and hidden equilibrium in transport models

Abstract

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 energy of the mapped system.

20 pages, 1 figure

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Duality and hidden symmetries in interacting particle systems
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory

Cited by in corpus (17)

• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Many-Body Open Quantum Systems
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• A reverse duality for the ASEP with open boundaries
• Exact solution of an integrable non-equilibrium particle system
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Integrable heat conduction model
• Duality in quantum transport models
• Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
• Exact physical quantities of a competing spin chain in the thermodynamic limit
• Steady state representations for the harmonic process
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas