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Understanding the Hamiltonian of mean force is key for open system thermodynamics. However, knowing only the probability density is insufficient, leading to ambiguity in stochastic thermodynamics constructions.

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Area of Science:

  • Statistical mechanics
  • Thermodynamics
  • Physical chemistry

Background:

  • Classical statistical mechanics and equilibrium thermodynamics of open systems rely on the Hamiltonian of mean force.
  • The Hamiltonian of mean force determines the equilibrium phase space probability density for strongly coupled systems.

Purpose of the Study:

  • To investigate the relationship between the Hamiltonian of mean force and the probability density in open systems.
  • To explore the possibility of constructing stochastic thermodynamics from known thermodynamic structures.
  • To identify limitations and ambiguities in current theoretical frameworks.

Main Methods:

  • Formulation of classical statistical mechanics for open systems using the Hamiltonian of mean force.
  • Analysis of the sufficiency of probability density for determining the Hamiltonian of mean force.
  • Extension of thermodynamic structures to fluctuating quantities, forming stochastic thermodynamics.

Main Results:

  • The Hamiltonian of mean force uniquely determines the equilibrium phase space probability density.
  • Knowledge of the probability density alone is insufficient to determine the Hamiltonian of mean force.
  • Extending thermodynamic structures to stochastic thermodynamics is possible if the Hamiltonian of mean force is known, but introduces significant ambiguity.

Conclusions:

  • A lack of physical guiding principles hinders the selection of physically meaningful theories among ambiguous constructions.
  • Further research is needed to resolve the ambiguities in stochastic thermodynamics for strongly coupled open systems.
  • The current framework highlights a gap in understanding the fundamental underpinnings of open system thermodynamics.