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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Computational Physics

Background:

  • Studying work distributions in strongly nonequilibrium processes is challenging due to extremely small probabilities.
  • Traditional simulation methods struggle with probabilities as low as 10⁻²⁴⁰.

Purpose of the Study:

  • To develop and apply a general large-deviation approach for analyzing work distributions in various processes.
  • To accurately calculate free energy differences for a two-dimensional Ising system under varying external fields.

Main Methods:

  • Utilized a general large-deviation approach to study work distributions.
  • Applied the method to a critical 2D Ising system (128x128) with rapidly changing external fields (B=3 to 0).
  • Calculated free-energy differences from work distributions at extremely low probabilities.

Main Results:

  • Achieved high relative precision (10⁻⁴) in free energy calculations, validated against exact values.
  • Demonstrated the method's effectiveness for nonzero fields where umbrella sampling is inefficient.
  • Verified Crooks theorem for forward and backward processes with high precision.

Conclusions:

  • The large-deviation approach provides a powerful tool for calculating free energies in challenging nonequilibrium systems.
  • This method overcomes limitations of direct simulations for extremely small probability regimes.
  • The study successfully maps the free energy of an Ising magnet as a function of field strength.