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Linear response theory for thermodynamic properties.

J K Nielsen1

  • 1Department of Mathematics and Physics, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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A new fluctuation-dissipation theorem connects thermodynamic response functions to equilibrium fluctuations in the microcanonical ensemble. This framework, applicable beyond linear response, was demonstrated using simulations of a supercooled fluid.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Classical Mechanics

Background:

  • The fluctuation-dissipation theorem (FDT) traditionally relates equilibrium fluctuations to linear response functions.
  • Standard FDT formulations often rely on perturbations expressible as Hamiltonian terms, limiting applicability to certain systems.
  • Systems controlled by heat flow exhibit dissipation via entropy flow, a scenario not always covered by conventional linear response theory.

Purpose of the Study:

  • To derive a fluctuation-dissipation theorem applicable to the microcanonical ensemble from classical mechanics.
  • To extend the framework of thermodynamic response beyond the usual linear response schemes.
  • To analyze thermodynamic response functions in systems where dissipation is characterized by entropy flow.

Main Methods:

Related Experiment Videos

  • Derivation of a generalized fluctuation-dissipation theorem using classical mechanics.
  • Application of the derived theorem to analyze thermodynamic response.
  • Utilizing molecular dynamics simulations of a supercooled binary Lennard-Jones fluid to extract response functions.

Main Results:

  • A novel fluctuation-dissipation theorem is established for the microcanonical ensemble.
  • The full frequency-dependent thermodynamic response matrix was successfully extracted from simulations.
  • Supercooled binary Lennard-Jones fluid exhibited high relaxation strength across most response functions, with adiabatic compressibility being an exception.
  • Thermodynamic susceptibilities showed an increase at low frequencies as temperature decreased along an isochore.

Conclusions:

  • The derived fluctuation-dissipation theorem provides a broader framework for understanding thermodynamic response.
  • The study demonstrates the theorem's utility in analyzing complex systems like supercooled fluids.
  • Results highlight the temperature dependence of thermodynamic properties in supercooled liquids, offering insights into their dynamic behavior.