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Maximum speed of dissipation.

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This study establishes statistical-mechanical speed limits for irreversible processes in chaotic many-particle systems. These findings reveal fundamental trade-offs between dissipation rates and the time required for dynamic processes.

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Area of Science:

  • Statistical mechanics
  • Non-equilibrium thermodynamics
  • Chaos theory

Background:

  • Classical dynamics of many-particle systems are complex.
  • Understanding dissipation in non-equilibrium systems is crucial.
  • Deterministic fluctuation theorems provide a foundation for analyzing irreversible processes.

Purpose of the Study:

  • To derive statistical-mechanical speed limits on dissipation.
  • To establish fundamental constraints on the relationship between time and dissipation in physical systems.
  • To extend these limits to physical observables measuring dissipation rates.

Main Methods:

  • Derivation from classical, chaotic dynamics of many-particle systems.
  • Utilizing deterministic fluctuation theorems.
  • Analyzing systems interacting with deterministic thermostats.

Main Results:

  • Identified a speed limit related to entropy production: S[over ¯]_{e}/k_{B}≥1/2Δt.
  • Determined the minimum time for a process: Δt≥k_{B}/2S[over ¯]_{e}.
  • Revealed a trade-off between time and heat flux: Q[over ¯]Δt≥k_{B}T/2 for systems with deterministic thermostats.

Conclusions:

  • Statistical-mechanical speed limits constrain dissipation in non-stationary processes.
  • These bounds are applicable to transient dynamics and excursions from steady states.
  • The findings provide a theoretical framework for understanding time-dissipation relationships in complex systems.