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Generalized-ensemble simulations enhance free energy landscape sampling using replica transitions. This study revises techniques, deriving acceptance probability for non-instantaneous switches based on the Crooks nonequilibrium work theorem.

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Area of Science:

  • Computational Chemistry
  • Statistical Mechanics

Background:

  • Generalized-ensemble simulations, including replica exchange and serial methods, are vital for exploring complex free energy landscapes.
  • These methods enhance sampling by transitioning system replicas between different ensembles, controlled by parameters like temperature or collective variables.

Purpose of the Study:

  • To revise generalized-ensemble simulation techniques, focusing on their connection to the Crooks nonequilibrium work (CNW) theorem.
  • To derive the acceptance probability for non-instantaneous replica switches in serial generalized-ensemble simulations.

Main Methods:

  • Revision of generalized-ensemble simulation techniques within the framework of Markovian processes.
  • Derivation of acceptance probability for non-instantaneous switches, correlating with the CNW theorem.
  • Generalized relationship of the CNW theorem provided in terms of equilibrium probability distribution.

Main Results:

  • Explicit knowledge of time-dependent weight factors is not required for non-instantaneous switches in serial generalized-ensemble simulations.
  • A generalized CNW theorem is presented for equilibrium probability distributions.
  • Illustrative calculations on a toy model demonstrate distinct behaviors of instantaneous versus non-instantaneous replica transitions.

Conclusions:

  • Non-instantaneous replica switches offer a viable alternative in generalized-ensemble simulations, simplifying calculations by removing the need for explicit time-dependent weight factors.
  • The study provides a theoretical framework and practical demonstration for these advanced simulation techniques.