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Stochastic trajectories in Markovian systems exhibit time-reversal symmetry. This finding links trajectories with opposite entropy production rates, extending previous work on deterministic systems.

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Area of Science:

  • Statistical mechanics
  • Non-equilibrium thermodynamics
  • Stochastic processes

Background:

  • Deterministic systems have conditional reversibility theorems, like Gallavotti's.
  • Stochastic systems require a similar understanding for non-equilibrium dynamics.

Purpose of the Study:

  • Establish the stochastic counterpart to Gallavotti's conditional reversibility theorem.
  • Investigate the relationship between time-reversed trajectories and entropy production in Markovian systems.

Main Methods:

  • Utilizing an equivalence between conditioned (microcanonical) and biased (canonical) ensembles.
  • Analyzing discrete-state stochastic systems with Markovian dynamics.

Main Results:

  • Stochastic trajectories conditioned on opposite entropy production rates are related by time reversal in the long-time limit.
  • The probability of a trajectory with entropy production σ equals that of the time-reversed trajectory with entropy production -σ.

Conclusions:

  • The established theorem provides a fundamental link between forward and time-reversed processes in non-equilibrium stochastic systems.
  • This work extends the understanding of thermodynamic principles to stochastic dynamics, with potential applications in various physical systems.