On the nonequilibrium relation between potential and stationary distribution for driven diffusion

Abstract

We investigate the relation between an applied potential and the corresponding stationary state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for the relative density when the potential is locally perturbed, and inversely, we find that the potential needs to be wholly rearranged for the purpose of creating a locally changed density. The direct question, determining the density as a function of the potential, comes under the response theory out of equilibrium. The inverse problem of determining the potential that produces a given stationary distribution naturally arises in the study of dynamical fluctuations. This link to the fluctuation theory results in a variational characterization of the stationary density upon a given potential and vice versa.

11 pages; v2: slightly rewritten with 2 appendices and 3 references added

References in corpus (10)

• Steady state statistics of driven diffusions
• Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
• Long range correlations and phase transition in non-equilibrium diffusive systems
• Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics
• Brownian motion of finite-inertia particles in a simple shear flow
• Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models
• On the long range correlations of thermodynamic systems out of equilibrium
• Stochastic processes in turbulent transport
• Long range spatial correlation between two Brownian particles under external driving
• High-temperature expansion for steady nonequilibrium states in driven lattice gases

Cited by in corpus (11)

• A nonequilibrium extension of the Clausius heat theorem
• Thermodynamic formula for the cumulant generating function of time-averaged current
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• Rigorous meaning of McLennan ensembles
• How statistical forces depend on thermodynamics and kinetics of driven media
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Eigenspectra of solar active region long-period oscillations
• Case study on the identification and classification of small-scale flow patterns in flaring active region
• Categorization model of moving small-scale intensity enhancements in solar active regions
• Non-local response in a lattice gas under a shear drive
• Wide-band fluctuations of solar active regions probed with SHARP magnetograms