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Universal bounds on current fluctuations.

Patrick Pietzonka1, Andre C Barato2, Udo Seifert1

  • 1II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany.

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Researchers derived four universal bounds for current fluctuations in nonequilibrium steady states, offering new constraints for systems beyond the Gaussian regime. These bounds apply to entropy changes and individual currents, enhancing our understanding of complex systems.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Complex Systems

Background:

  • Understanding fluctuations in nonequilibrium steady states is crucial for characterizing system dynamics.
  • Existing bounds often rely on Gaussian assumptions or specific system properties.

Purpose of the Study:

  • To derive universal bounds for current fluctuations in Markovian processes beyond the Gaussian regime.
  • To provide new constraints for entropy changes and individual currents in nonequilibrium systems.

Main Methods:

  • Derivation of four distinct universal bounds.
  • Numerical verification for parabolic and network-topology-dependent bounds.
  • Rigorous proof for an exponential bound.
  • Analysis of an asymptotic bound for large fluctuations.

Main Results:

  • Four universal bounds for current fluctuations were derived, applicable beyond the Gaussian regime.
  • A parabolic bound depends on average entropy production; a stronger bound includes thermodynamic forces and network topology.
  • A rigorously proved exponential bound depends on average entropy production and transition rates.
  • An asymptotic bound predicts the generating function's growth for large fluctuations.

Conclusions:

  • The derived bounds offer a general class of constraints for nonequilibrium systems.
  • The parabolic bound was shown to be valid for driven diffusive systems.
  • These findings advance the theoretical framework for analyzing fluctuations in complex systems.