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The General Equation for Non-Equilibrium Reversible Irreversible Coupling (generic) framework is enhanced to account for external forces. This modification ensures thermodynamic consistency and energy conservation in complex systems.

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Area of Science:

  • Statistical Mechanics
  • Non-Equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • The General Equation for Non-Equilibrium Reversible Irreversible Coupling (generic) framework offers a thermodynamically consistent method for modeling coarse-grained variables.
  • This framework ensures energy conservation and entropy increase via Markovian dynamic equations.
  • External time-dependent forces can disrupt energy conservation, necessitating framework adjustments.

Purpose of the Study:

  • To modify the generic framework to incorporate external time-dependent forces.
  • To ensure thermodynamic consistency under external forcing conditions.
  • To provide a rigorous statistical mechanics foundation for the modified framework.

Main Methods:

  • Derivation of an exact transport equation for coarse-grained variables using a projection operator technique.
  • Application of the Markovian approximation to the derived transport equation.
  • Analysis of the modified framework's structure under external forcing.

Main Results:

  • A modified generic framework that accurately accounts for external time-dependent forces.
  • Demonstration that the modified framework preserves thermodynamic consistency (energy conservation and entropy increase).
  • Establishment of the statistical mechanics underpinnings for the generic framework with external forcing.

Conclusions:

  • The developed approach successfully extends the generic framework to systems subjected to external forces.
  • The modified framework maintains thermodynamic laws, crucial for accurate modeling of non-equilibrium systems.
  • This work provides a robust theoretical tool for studying complex systems with time-dependent external influences.