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Time-dependent fluctuation theorem.

Emil Mittag1, Denis J Evans

  • 1Research School of Chemistry, The Australian National University, Canberra Australian Capital Territory 0200, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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The fluctuation theorem (FT) extends the second law of thermodynamics to small systems. This study introduces a time-dependent FT for dissipative systems, confirming its link to time-reversal symmetry and thermodynamics.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • The fluctuation theorem (FT) generalizes the second law of thermodynamics for small systems and short observation times.
  • For thermostated systems, FT quantifies entropy production versus consumption probability ratios.

Purpose of the Study:

  • To propose and test a time-dependent fluctuation theorem (FT) for dissipative systems subjected to time-dependent fields.
  • To investigate the connection between time-reversal symmetry, FT, and the second law of thermodynamics in these systems.

Main Methods:

  • Development of a time-dependent fluctuation theorem applicable to thermostated dissipative systems.
  • Experimental or computational testing of the proposed FT using time-reversible dynamical systems.

Related Experiment Videos

  • Analysis of trajectory sets and their time-integrated entropy production values.

    • Main Results:

    • The proposed time-dependent FT was successfully tested on dissipative systems.
    • Evidence was found that trajectories with conjugate entropy production values are time-reversal images.
    • A deep connection between time-reversal symmetry, FT, and the second law was verified.

    Conclusions:

    • The study validates a new version of the fluctuation theorem for time-dependent processes in dissipative systems.
    • The findings reinforce the fundamental relationship between time-reversibility and thermodynamic laws.
    • This work advances the understanding of entropy production in non-equilibrium statistical mechanics.