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We discovered a trade-off between how fast systems change and their entropy production in classical stochastic Markov processes. Dynamical activity, a measure of system movement, is key to this fundamental physical relationship.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Classical stochastic Markov processes are fundamental to understanding systems with inherent randomness.
  • The local detailed balance condition is a key assumption in many thermodynamic analyses.
  • Entropy production quantifies irreversibility and energy dissipation in dynamic systems.

Purpose of the Study:

  • To investigate the speed limit of state transformations in classical stochastic Markov processes.
  • To explore the relationship between speed, entropy production, and dynamical activity.
  • To analyze these relationships both with and without the local detailed balance condition.

Main Methods:

  • Analysis of classical stochastic Markov processes.
  • Derivation of trade-off inequalities relating state transformation speed and entropy production.
  • Inclusion of dynamical activity as a crucial factor.
  • Utilizing Hatano-Sasa entropy production for systems without local detailed balance.

Main Results:

  • A trade-off inequality between transformation speed and entropy production exists for both cases (with and without local detailed balance).
  • Dynamical activity, linked to a time scale, is integral to these inequalities.
  • The Hatano-Sasa entropy production is employed for processes deviating from local detailed balance.

Conclusions:

  • The derived inequalities provide fundamental insights into the physical mechanisms governing stochastic processes.
  • These findings offer a unified perspective on speed limits and irreversibility in thermodynamics.
  • The results highlight the importance of dynamical activity in understanding energy dissipation and process efficiency.