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Fluctuation-dissipation theorem for metastable systems.

G Báez1, H Larralde, F Leyvraz

  • 1Centro de Ciencias Físicas UNAM, AP 48-3, 62210, Cuernavaca, Morelos, México. baez@fis.unam.mx

Physical Review Letters
|April 12, 2003
PubMed
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The fluctuation-dissipation theorem holds for Markovian systems before nucleation time. This is demonstrated by modeling systems as superpositions of ground and excited states, verified numerically for the Ising model.

Area of Science:

  • Statistical mechanics
  • Theoretical physics
  • Condensed matter physics

Background:

  • The fluctuation-dissipation theorem (FDT) is a fundamental concept linking microscopic fluctuations to macroscopic dissipation.
  • Its applicability in systems with metastable states, particularly concerning nucleation phenomena, requires careful examination.
  • Markovian systems satisfying detailed balance are common models in statistical physics.

Purpose of the Study:

  • To establish the validity of a generalized fluctuation-dissipation theorem (FDT) for Markovian systems with metastable states.
  • To determine the temporal regime where this generalized FDT holds, specifically relative to the nucleation time.
  • To provide a theoretical framework and numerical validation for the FDT in such systems.

Main Methods:

Related Experiment Videos

  • Defining a generalized fluctuation-dissipation theorem connecting generalized susceptibilities and time correlation functions.
  • Modeling Markovian systems satisfying detailed balance as a superposition of the ground and first excited states of the master equation.
  • Performing numerical simulations on a two-dimensional Ising model to corroborate the theoretical findings.

Main Results:

  • The generalized fluctuation-dissipation theorem is shown to be valid for times shorter than the nucleation time of the metastable state.
  • The theoretical framework successfully describes the behavior of systems near metastable states.
  • Numerical results for the two-dimensional Ising model confirm the predicted validity range of the FDT.

Conclusions:

  • The fluctuation-dissipation theorem, when appropriately defined, is applicable to Markovian systems exhibiting metastability, up to the nucleation time.
  • The superposition of ground and first excited states provides a valid approximation for these systems.
  • This work offers a deeper understanding of non-equilibrium statistical mechanics and the dynamics of metastable states.