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Statistical mechanics in the extended Gaussian ensemble.

Ramandeep S Johal1, Antoni Planes, Eduard Vives

  • 1Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain. rjohal@ecm.ub.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

The extended Gaussian ensemble (EGE) offers a new statistical mechanics framework. It allows independent control over energy and fluctuations, generalizing the canonical ensemble for broader applications.

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Quantum Physics

Background:

  • The canonical ensemble is a fundamental concept in statistical mechanics.
  • Existing models may not fully capture systems with independent control over energy and fluctuations.
  • Generalizations of standard ensembles are crucial for advancing theoretical physics.

Purpose of the Study:

  • Introduce the extended Gaussian ensemble (EGE) as a novel generalization of the canonical ensemble.
  • Develop a statistical mechanical formalism for the EGE.
  • Explore the properties and applications of the EGE.

Main Methods:

  • Derivation of the statistical mechanical formalism using system-reservoir analysis and maximum entropy principle.
  • Identification of two key parameters (beta and gamma) controlling mean energy and energy fluctuations.

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  • Establishment of Legendre transform structure and a stability criterion for the EGE.

    • Main Results:

    • The EGE probability distribution depends on parameters beta and gamma, enabling independent tuning of mean energy and energy fluctuations.
    • A generalized thermodynamic potential and stability criterion were established for the EGE.
    • Comparison of the EGE distribution with the q-exponential distribution was performed.

    Conclusions:

    • The extended Gaussian ensemble provides a flexible framework for statistical mechanics.
    • The EGE formalism allows for independent control over system energy and fluctuations.
    • The presented framework has potential applications in systems like independent spins.