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Weak additivity principle for current statistics in d dimensions.

C Pérez-Espigares1, P L Garrido2, P I Hurtado2

  • 1University of Modena and Reggio Emilia, via G. Campi 213/b, 41125 Modena, Italy.

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Summary
This summary is machine-generated.

We extend the additivity principle (AP) to d-dimensional driven diffusive systems. The weak AP better minimizes the macroscopic fluctuation theory action for current statistics in higher dimensions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Non-equilibrium Systems

Background:

  • The additivity principle (AP) simplifies current distribution calculations in 1D non-equilibrium systems.
  • Extending these principles to higher dimensions is crucial for understanding complex physical phenomena.

Purpose of the Study:

  • To generalize the additivity principle (AP) to d-dimensional driven diffusive systems.
  • To validate the extended AP against numerical and exact microscopic calculations in 2D systems.

Main Methods:

  • Extension of the additivity principle (AP) to general d-dimensions.
  • Numerical simulations of rare events in 2D diffusive systems.
  • Microscopic exact calculations for paradigmatic 2D diffusive transport models.

Main Results:

  • The additivity principle (AP) is successfully extended to d-dimensional driven diffusive systems.
  • A structured current vector field and local mobility are essential for understanding current statistics in d>1.
  • The weak AP provides a better minimizer for the macroscopic fluctuation theory action compared to the straightforward extension.

Conclusions:

  • The additivity principle (AP) can be generalized to higher dimensions, offering a powerful tool for non-equilibrium statistical mechanics.
  • Understanding the interplay between current vector fields and local mobility is key in d>1 systems.
  • The weak AP offers improved accuracy for current statistics in macroscopic fluctuation theory.