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

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Condensed Matter Physics

Background:

• Understanding steady states in open systems is crucial.
• Previous work predicted long-range correlations in non-equilibrium steady states (NESS) using fluctuating hydrodynamics.
• Experimental observations have supported these predictions.

Purpose of the Study:

• To develop an exact expression for the probability of macroscopic density profiles in NESS.
• To generalize the concept of free energy density to non-equilibrium systems.
• To provide a theoretical framework for understanding long-range correlations in NESS.

Main Methods:

• Considered an open system with matter flux between reservoirs at different chemical potentials.
• Analyzed the probability of macroscopic density profiles rho(x) for a large system size N.
• Derived an exact expression for a generalized free energy density functional F([rho]).

Main Results:

• The probability of a density profile rho(x) is given by exp[-NF([rho])].
• The derived functional F([rho]) is nonlocal.
• This nonlocal functional accurately captures the long-range correlations observed in NESS.

Conclusions:

• The generalized free energy functional provides a powerful tool for studying NESS.
• The findings confirm and theoretically ground previous predictions and experimental observations of long-range correlations.
• This work advances the understanding of statistical mechanics in non-equilibrium conditions.