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Large deviation function and fluctuation theorem for classical particle transport.

Upendra Harbola1, Christian Van den Broeck2, Katja Lindenberg3

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Summary
This summary is machine-generated.

This study analyzes particle transfer between reservoirs, revealing conditions for the steady-state fluctuation theorem. The theorem holds when particle number distributions decay exponentially, ensuring system analyticity.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Transport Phenomena

Background:

  • Understanding particle and energy transfer in classical systems is crucial for thermodynamics.
  • Non-equilibrium systems exhibit complex dynamics not captured by traditional equilibrium theories.
  • Fluctuation theorems provide insights into the statistical behavior of systems far from equilibrium.

Purpose of the Study:

  • To analytically evaluate the large deviation function for classical particle transfer.
  • To determine the conditions under which the steady-state fluctuation theorem is valid.
  • To explore the relationship between initial conditions and the attainment of long-time asymptotic regimes.

Main Methods:

  • Analytical evaluation of the large deviation function.
  • Modeling classical particle transfer between two reservoirs.
  • Analysis of initial conditions and their impact on system evolution.
  • Investigation of particle number distribution decay rates.

Main Results:

  • The asymptotic long-time regime was reached from a specific propagating initial condition.
  • The steady-state fluctuation theorem was shown to hold under specific conditions.
  • Analyticity of the generating function and a discrete spectrum for the evolution operator are implied by faster-than-exponential decay of particle number distributions.

Conclusions:

  • The study provides analytical insights into non-equilibrium statistical mechanics.
  • Conditions for the validity of the steady-state fluctuation theorem in classical particle transfer models were established.
  • The findings link system properties like analyticity and spectral properties to observable behaviors such as distribution decay rates.