Monte Carlo entropic sampling for the study of metastable states and relaxation paths

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Abstract
We present a continuous extension of the recent Monte Carlo entropic method for sampling a density of states restricted in dimensionless macroscopic parameters. The method performs a random walk through a two-dimensional macrostate space and provides complete information in the form of continuous functions of the system’s coupling constants. For the example of an Ising system, we project relaxation paths from Monte Carlo Metropolis dynamic over the two-dimensional state space and compare them with a “most probable path” associated with the equilibrium distribution, derived from the density of states. We observe a close agreement between them in the stochastic regime, i.e., before the system escapes from the metastable state. We establish a Markovian macroscopic dynamic over the two macroscopic parameters and we discuss it with respect to the Metropolis microscopic dynamic.