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Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Theoretical Physics

Background:

  • Continuous-time Markov chains are fundamental in modeling dynamic systems.
  • Understanding nonequilibrium statistical mechanics is crucial for analyzing complex systems.
  • Effective affinity is a key parameter in quantifying system dynamics.

Purpose of the Study:

  • To determine the probability of negative edge current in continuous-time Markov chains.
  • To generalize the 'noria' formula to multicyclic networks.
  • To provide operational insights into effective affinity and its estimators.

Main Methods:

  • A constructive first-transition approach was employed.
  • Analysis of effective affinity and its relation to current negativity.
  • Comparison of various estimators for assessing nonequilibrium properties.

Main Results:

  • The probability of edge current becoming negative is proven to be 1 or 0 based on effective affinity thresholds.
  • The study generalizes the 'noria' formula to multicyclic networks.
  • Stopping problems are suggested as potentially more accurate for assessing nonequilibrium nature.

Conclusions:

  • The findings offer a precise condition for negative edge current in Markov chains.
  • The research extends existing formulas to more complex network structures.
  • New perspectives on quantifying and assessing system nonequilibrium are presented.