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Entropy Change in Reversible Processes01:10

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Upper bound for entropy production in Markov processes.

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This study introduces novel upper bounds for entropy production in stochastic thermodynamics, contrasting with existing lower bounds. These findings offer new insights into the second law of thermodynamics and its applications.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • The second law of thermodynamics dictates non-negative entropy production.
  • Recent advances in stochastic thermodynamics introduced refined laws with lower bounds on entropy production.
  • Existing research focuses on lower bounds, leaving upper bounds less explored.

Purpose of the Study:

  • To derive and present novel upper bounds for entropy production in stochastic systems.
  • To establish bounds based on dynamical activity and maximum transition-rate ratio.
  • To extend thermodynamic principles to non-equilibrium and time-dependent systems.

Main Methods:

  • Derivation of two distinct upper bounds for entropy production.
  • Application of bounds to steady-state conditions.
  • Application of bounds to arbitrary time-dependent conditions.
  • Validation through numerical simulations.

Main Results:

  • Two new upper bounds for entropy production were successfully derived.
  • One bound is applicable to steady-state systems.
  • The second bound is valid for time-dependent systems.
  • Numerical simulations confirmed the validity of the derived bounds.

Conclusions:

  • The study successfully established upper bounds for entropy production, complementing existing lower bounds.
  • These findings provide new constraints and insights into the second law of thermodynamics.
  • Potential applications in various fields of non-equilibrium statistical physics were identified.