Nonequilibrium thermodynamic potentials for continuous-time Markov chains

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Nonlinear Dynamics

Background:

• Equilibrium (EQ) processes exhibit rare fluctuations.
• Nonequilibrium (NE) stationary processes have typical fluctuations.
• Large deviation theory provides a framework to analyze rare events.

Purpose of the Study:

• To connect fluctuations in equilibrium and nonequilibrium systems.
• To introduce and define new nonequilibrium thermodynamic potentials.
• To establish a theoretical framework for understanding NE systems.

Main Methods:

• Utilizing large deviation theory.
• Analyzing continuous-time Markov chains.
• Developing two new NE ensembles (fixed dynamics/fluctuating variables and fixed variables/fluctuating dynamics).

Main Results:

• Identified conjugated variables for NE processes.
• Demonstrated the Legendre duality between NE potentials and conditioned EQ processes.
• Found a variational principle for NE potentials, yielding NE equations of state and Maxwell relations.

Conclusions:

• Nonequilibrium processes can be understood through conditioned equilibrium processes.
• The introduced NE potentials generalize thermodynamic concepts to NE systems.
• The findings extend Onsager reciprocity relations to a broader class of systems.