Microcanonical ensemble out of equilibrium

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Information Theory

Background:

• The microcanonical ensemble is fundamental to equilibrium thermodynamics.
• The principle of maximum caliber describes system trajectories but lacks physical justification.
• Open questions exist regarding the microscopic origin and choice of observables for this principle.

Purpose of the Study:

• To investigate the microscopic origin and physical interpretation of the maximum caliber approach.
• To determine the guiding principles for selecting relevant observables in nonequilibrium systems.
• To extend Boltzmann's method to a microcanonical caliber principle for trajectory analysis.

Main Methods:

• Extension of Boltzmann's method to a microcanonical caliber principle.
• Counting equally probable realizations of system trajectories.
• Maximizing microcanonical caliber under imposed constraints.

Main Results:

• Systematic development of generalized local detailed-balance relations.
• Clarification of statistical origins for inhomogeneous transport.
• Independent derivation of key stochastic thermodynamics equations.
• Introduction of a dynamical ensemble theory for nonequilibrium steady states.

Conclusions:

• The microcanonical caliber principle provides a dynamical ensemble theory for nonequilibrium systems.
• The framework clarifies transport origins and derives stochastic thermodynamics equations.
• This approach offers insights into systems deviating from standard thermodynamic conditions.