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Speed limits for discrete-time Markov chains.

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This study explores thermodynamic speed limits in discrete-time Markov chains, finding that time-reversed entropy production (EP) meets the speed limit, unlike time-backward EP. New practical limits are derived for specific systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Thermodynamic speed limits define the minimum entropy production (EP) for state transitions.
  • Existing speed limits are established for continuous-time Markov processes.
  • Application of speed limits to discrete-time Markov chains is an unexplored area.

Purpose of the Study:

  • To investigate thermodynamic speed limits in discrete-time Markov chains.
  • To analyze two common measures of irreversibility: time-reversed EP and time-backward EP.
  • To derive practical speed limits for specific discrete-time systems.

Main Methods:

  • Analysis of entropy production in discrete-time Markov chains.
  • Comparison of time-reversed EP and time-backward EP against speed limit criteria.
  • Derivation of novel speed limits for cyclic or unidirectional transition systems.
  • Validation through toy models, cell-state dynamics, and theoretical computations.

Main Results:

  • Time-reversed entropy production satisfies the speed limit in discrete-time Markov chains.
  • Time-backward entropy production does not satisfy the speed limit.
  • New practical speed limits derived for time-reversed EP are applicable to cyclic or unidirectional systems.
  • Results are shown to generalize to continuous-time Markov processes.

Conclusions:

  • The study establishes the validity of thermodynamic speed limits for time-reversed entropy production in discrete-time Markov chains.
  • The findings extend the applicability of speed limits to systems where conventional limits fail.
  • The derived relations offer new insights into the fundamental constraints of non-equilibrium processes.