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Echo states for detailed fluctuation theorems.

T Becker1, T Willaert1, B Cleuren1

  • 1Hasselt University, B-3590 Diepenbeek, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
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Summary
This summary is machine-generated.

Detailed fluctuation theorems reveal how entropy production probabilities change under transformed dynamics. For specific initial conditions (echo states), these theorems connect direct and transformed process entropy production, as shown in quantum dot simulations.

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Area of Science:

  • Statistical Mechanics
  • Quantum Thermodynamics
  • Non-equilibrium Physics

Background:

  • Detailed fluctuation theorems analyze stochastic entropy production along dynamic trajectories.
  • These theorems often involve transformed dynamics like time reversal or adjoint operations.
  • Understanding the conditions under which these theorems hold is crucial for non-equilibrium statistical mechanics.

Purpose of the Study:

  • To identify specific initial conditions, termed 'echo states', that simplify detailed fluctuation theorems.
  • To establish a direct relationship between entropy production in original and transformed dynamics.
  • To demonstrate these findings using a model system.

Main Methods:

  • Theoretical analysis of fluctuation theorems under transformed dynamics.
  • Identification and characterization of 'echo states' as unique initial conditions.
  • Analytical calculations and numerical simulations on a modulated two-state quantum dot.

Main Results:

  • Discovered 'echo states' where the final distribution of transformed dynamics matches the initial distribution.
  • Demonstrated that detailed fluctuation theorems directly relate entropy production of direct and transformed processes at echo states.
  • Validated these results through explicit analytical and numerical studies of a quantum dot system.

Conclusions:

  • Echo states provide a powerful simplification for applying detailed fluctuation theorems.
  • The findings offer new insights into the behavior of entropy production in non-equilibrium systems.
  • The quantum dot model serves as a concrete example of these theoretical developments.