Expression for the stationary distribution in nonequilibrium steady states

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Stochastic Processes

Background:

• Understanding non-equilibrium steady states is crucial in various scientific fields.
• Stochastic systems interacting with multiple heat baths present complex behaviors.
• Existing models often lack precision for higher-order thermodynamic forces.

Purpose of the Study:

• To derive precise expressions for the stationary distribution of general stochastic systems in non-equilibrium steady states.
• To extend the detailed fluctuation theorem to systems coupled with multiple heat baths.
• To provide a foundation for experimental verification in mesoscopic systems.

Main Methods:

• Utilizing the detailed fluctuation theorem.
• Deriving expressions for the stationary distribution up to the second order in thermodynamic forces.
• Analyzing excess entropy changes and heat transfer in conditioned path ensembles.

Main Results:

• Concise expressions for the stationary distribution were derived.
• The probability of a microstate eta is proportional to exp[Phi(eta)], where Phi(eta) is the excess entropy change.
• The results are accurate up to the second order in thermodynamic forces.

Conclusions:

• The derived expressions offer a more accurate description of non-equilibrium steady states.
• The findings can be extended to systems driven by other sources, like particle currents.
• Experimental verification in mesoscopic systems is feasible.