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Related Experiment Videos

Path integrals and fluctuations in irreversible thermodynamics.

A J McKane1, F Vázquez

  • 1Theory Group, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

We developed a new path-integral method to analyze stochastic fluctuations in linear irreversible thermodynamics. This approach overcomes issues with singular correlation matrices, enabling broader applications in statistical physics.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Thermodynamics

Background:

  • Stochastic differential equations model fluctuations in linear irreversible thermodynamics.
  • Standard path-integral formulations fail when stochastic terms have singular correlation matrices.

Purpose of the Study:

  • To develop a generalized path-integral representation for stochastic differential equations.
  • To apply this method to linearized irreversible thermodynamics and density fluctuations in fluids.

Main Methods:

  • Constructed a path-integral representation valid for singular correlation matrices.
  • Calculated response and correlation functions for density fluctuations.

Main Results:

  • Successfully formulated path integrals for systems with singular correlation matrices.

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  • Explicitly computed response and correlation functions for fluid density fluctuations.

    • Conclusions:

    • The generalized path-integral technique is applicable to linearized irreversible thermodynamics.
    • This method provides a robust framework for analyzing fluctuations in various non-equilibrium systems.