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This study introduces a microcanonical caliber principle, extending Boltzmann

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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.