Free Energy Differences in Nonequilibrium Thermodynamic Processes

Area of Science:

• Non-equilibrium statistical mechanics
• Quantum thermodynamics

Background:

• Recent interest in systems allowed to deviate from equilibrium.
• Need for quantities describing non-equilibrium processes.

Purpose of the Study:

• Formulate a quantity whose average depends only on initial and final states for non-equilibrium systems.
• Generalize this to non-equilibrium initial and final states.
• Explore quantum analogues and thermodynamic implications.

Main Methods:

• Formulation of a novel average quantity.
• Development of generalized relations for non-equilibrium states.
• Derivation of quantum analogues.

Main Results:

• A quantity is defined whose ensemble average is state-independent during non-equilibrium processes.
• Generalizations are established for arbitrary initial and final states.
• Quantum versions of these relations are derived.

Conclusions:

• The developed quantity provides a new tool for studying non-equilibrium systems.
• The findings offer insights into entropy increase in thermodynamics.
• Quantum analogues suggest broader applicability in quantum statistical mechanics.