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Long-range interacting systems in the unconstrained ensemble.

Ivan Latella1, Agustín Pérez-Madrid2, Alessandro Campa3

  • 1Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, 2 Avenue Augustin Fresnel, 91127 Palaiseau Cedex, France.

Physical Review. E
|February 18, 2017
PubMed
Summary
This summary is machine-generated.

Systems with long-range interactions can achieve thermodynamic equilibrium in completely open systems (unconstrained ensemble). This contrasts with short-range systems, which cannot reach equilibrium under these conditions.

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Area of Science:

  • Statistical mechanics
  • Thermodynamics
  • Condensed matter physics

Background:

  • Completely open systems exchange heat, work, and matter with their environment.
  • Equilibrium states in open systems are defined by temperature, pressure, and chemical potential.
  • The unconstrained ensemble describes these open systems, using replica energy as the relevant free energy.

Purpose of the Study:

  • To investigate the conditions under which systems can reach thermodynamic equilibrium in the unconstrained ensemble.
  • To determine if long-range interacting systems differ from short-range systems in their ability to attain equilibrium in open systems.
  • To compare the unconstrained ensemble with canonical and grand-canonical ensembles for systems with varying interaction ranges.

Main Methods:

  • Analysis of the unconstrained ensemble for systems with short-range and long-range interactions.
  • Utilizing a modified Thirring model to illustrate the findings.
  • Comparison of equilibrium configurations across different ensembles (unconstrained, canonical, grand-canonical).

Main Results:

  • Macroscopic systems with short-range interactions cannot achieve equilibrium in the unconstrained ensemble.
  • Systems with long-range interactions can attain thermodynamic equilibrium in the unconstrained ensemble.
  • Constraining ensembles (e.g., fixing volume or particle number) expands the parameter space for equilibrium configurations.

Conclusions:

  • Long-range interactions are crucial for enabling thermodynamic equilibrium in completely open systems.
  • The degree of ensemble constraint influences the accessibility of equilibrium states.
  • Findings highlight the importance of interaction range in statistical mechanics and thermodynamics.