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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Thermodynamic fluctuations and their lower bounds are crucial in non-equilibrium systems.
  • The nature of time (discrete vs. continuous) impacts the behavior of these fluctuations.
  • Markov chains and master equations are standard models for describing time evolution.

Purpose of the Study:

  • To investigate the physical reasons behind differing current fluctuations in discrete-time and continuous-time systems.
  • To establish a connection between fluctuation properties in discrete and continuous time formulations.
  • To derive unified uncertainty bounds for thermodynamic currents.

Main Methods:

  • Comparison of current fluctuations in discrete-time Markov chains and continuous-time master equations.
  • Development of a mathematical mapping between the moments of currents in discrete and continuous time.
  • Application of the mapping to derive generalized uncertainty bounds.

Main Results:

  • Current fluctuations are consistently higher in continuous-time master equations compared to discrete-time Markov chains.
  • Random transition timings in continuous time are identified as the primary cause for increased fluctuations.
  • A direct mapping between discrete and continuous time current moments was established.

Conclusions:

  • The nature of time significantly influences thermodynamic current fluctuations.
  • The established mapping provides a unified framework for calculating uncertainty bounds across different time formalisms.
  • This work simplifies the problem of determining uncertainty bounds for thermodynamic currents.