Generalized Ensemble and Tempering Simulations: A Unified View
arXiv:cond-mat/0605408 · doi:10.1103/PhysRevE.75.026109
Abstract
From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the form of a one-dimensional Fokker-Planck equation or a hopping process on a one-dimensional chain. In particular, we discuss the conditions under which these representations are valid approximate Markovian descriptions of the random walk in order parameter or control parameter space. They allow a unified discussion of the stationary distribution on, as well as of the stationary flow across each space. We demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space, and discuss the consequences of our results for optimizing simulations. Finally, we point out the limitations of these representations under conditions of broken ergodicity.
11 pages Latex, 2 eps figures, revised version, typos corrected, PRE in press
References in corpus (11)
- An efficient, multiple range random walk algorithm to calculate the density of states
- Exchange Monte Carlo Method and Application to Spin Glass Simulations
- Parallel Tempering Algorithm for Conformational Studies of Biological Molecules
- Feedback-optimized parallel tempering Monte Carlo
- Optimized parallel tempering simulations of proteins
- Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
- Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
- Generalized-ensemble Monte carlo method for systems with rough energy landscape
- Multicanonical Recursions
- The incomplete beta function law for parallel tempering sampling of classical canonical systems
- Flat Histogram Method of Wang-Landau and N-fold Way
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