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This study maps non-equilibrium random sequential addition processes to equilibrium systems using the replica method. This allows for theoretical predictions of non-equilibrium structural properties, validated by simulations.

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Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Materials Science

Background:

  • Many physical processes are non-equilibrium, yet theory and modeling lag behind equilibrium systems.
  • Equilibrium statistical mechanics offers powerful theoretical tools.
  • Mapping non-equilibrium systems to equilibrium analogs enables analysis with standard methods.

Purpose of the Study:

  • To revisit and apply the replica method for mapping non-equilibrium random sequential addition onto equilibrium systems.
  • To enable theoretical predictions of structural quantities in non-equilibrium processes.

Main Methods:

  • Utilizing the replica method to establish an equilibrium analog for non-equilibrium random sequential addition.
  • Comparing theoretical predictions with numerical simulations of the random sequential addition process.

Main Results:

  • The replica method successfully maps non-equilibrium random sequential addition to an equilibrium multi-component mixture.
  • Theoretical predictions for non-equilibrium structural quantities align with simulation results.

Conclusions:

  • The replica method provides a viable theoretical framework for studying non-equilibrium systems.
  • This approach facilitates the prediction and understanding of structural properties in non-equilibrium phenomena.