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Continuous-time random walk for open systems: fluctuation theorems and counting statistics.

Massimiliano Esposito1, Katja Lindenberg

  • 1Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This summary is machine-generated.

Continuous-time random walks (CTRW) in open systems have fluctuation theorems for trajectory quantities. However, these theorems only apply to trajectory entropy changes under specific conditions on waiting time distributions (WTDs).

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • Open systems exchange energy and matter with their environment.
  • Continuous-time random walks (CTRW) model particle or energy movement.
  • Waiting time distributions (WTDs) characterize the time between steps in CTRW.

Purpose of the Study:

  • To investigate fluctuation theorems for CTRW in open systems.
  • To determine conditions under which trajectory quantities represent entropy changes.
  • To analyze the long-time behavior of energy and matter transfers.

Main Methods:

  • Analysis of fluctuation theorems for CTRW.
  • Characterization of waiting time distributions (WTDs) using parameter alpha.
  • Examination of trajectory quantities and their relation to entropy change.
  • Derivation of long-time scaling for energy and matter transfers.

Main Results:

  • A fluctuation theorem for trajectory quantity R holds for any CTRW.
  • R equals trajectory entropy change only for separable WTDs with alpha=1.
  • For non-separable WTDs (alpha=1), entropy change fluctuation theorems hold only at long times.
  • No meaningful fluctuation theorem can be derived for WTDs with 0
  • Nth moments of energy/matter transfers scale as t^(n*alpha) at long times.

Conclusions:

  • The validity of fluctuation theorems for entropy changes in CTRW depends critically on WTD properties.
  • The parameter alpha in WTDs governs the applicability of fluctuation theorems and the scaling of transfers.
  • The study provides insights into the thermodynamics of open systems and transport phenomena.