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Related Experiment Videos

Non-Hamiltonian equilibrium statistical mechanics.

Alessandro Sergi1

  • 1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada ON M5S 3H6. asergi@chem.utoronto.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary

This study introduces an algebraic bracket to formulate equilibrium statistical mechanics for non-Hamiltonian systems. This new approach reveals that phase space compressibility breaks time-reversal invariance in these systems.

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Area of Science:

  • Statistical Mechanics
  • Non-Hamiltonian Systems
  • Classical Dynamics

Background:

  • Traditional statistical mechanics relies on Hamiltonian systems.
  • Non-Hamiltonian systems present challenges in formulating equilibrium statistical mechanics.
  • Previous work (Phys. Rev. E 64, 056125) established an approach for non-Hamiltonian dynamics.

Purpose of the Study:

  • To formulate equilibrium statistical mechanics for non-Hamiltonian systems using a generalized algebraic bracket.
  • To investigate the implications of this formulation on fundamental dynamical properties like time translation and time-reversal invariance.
  • To rederive the Liouville equation and analyze statistical averages, time correlation functions, and linear response theory within this framework.

Main Methods:

Related Experiment Videos

  • Introduction of a novel algebraic bracket to define non-Hamiltonian equations of motion in classical phase space.
  • Analysis of the properties of the generalized bracket, specifically the violation of the Jacobi identity.
  • Examination of the consequences of non-zero phase space compressibility on dynamical symmetries.

    • Main Results:

    • The generalized bracket does not satisfy the Jacobi identity, leading to a loss of time translation invariance for phase space functions.
    • Non-zero phase space compressibility breaks the time-reversal invariance of the dynamics.
    • The general Liouville equation is rederived, and properties of statistical averages are clarified.

    Conclusions:

    • The proposed algebraic bracket provides a consistent framework for the equilibrium statistical mechanics of non-Hamiltonian systems.
    • The findings highlight the breakdown of fundamental symmetries (time translation and time-reversal) due to the non-Hamiltonian nature and phase space compressibility.
    • The study lays the groundwork for further investigations into the statistical properties and response theories of complex non-Hamiltonian systems.