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Nonequilibrium equalities in absolutely irreversible processes.

Yûto Murashita1, Ken Funo1, Masahito Ueda1

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This summary is machine-generated.

This study extends nonequilibrium integral equalities to absolutely irreversible processes where standard fluctuation theorems fail. We identify mathematical singularities in probability measures as the cause and validate our findings in multiple models.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • Conventional integral fluctuation theorems apply to systems where forward and backward paths have non-zero probabilities.
  • Absolutely irreversible processes, characterized by vanishing forward-path probability and diverging entropy production, pose a challenge to existing theorems.
  • Understanding these extreme conditions is crucial for advancing non-equilibrium statistical mechanics.

Purpose of the Study:

  • To generalize nonequilibrium integral equalities to encompass absolutely irreversible processes.
  • To identify the mathematical basis of absolute irreversibility.
  • To validate the extended equalities using model systems.

Main Methods:

  • Generalization of nonequilibrium integral equalities.
  • Analysis of probability measure singularities.
  • Application to selected theoretical models.

Main Results:

  • Developed new integral equalities applicable to absolutely irreversible processes.
  • Identified probability measure singularity as the mathematical origin of absolute irreversibility.
  • Demonstrated the validity of the generalized equalities across various models.

Conclusions:

  • The generalized equalities provide a framework for studying systems with absolute irreversibility.
  • The findings offer new insights into the behavior of entropy production in extreme non-equilibrium conditions.
  • This work advances the theoretical understanding of statistical mechanics for irreversible processes.