Masayuki Ohzeki, Akihisa Ichiki
Monte-Carlo method is a major technique to investigate equilibrium properties governed by the well-known Gibbs-Boltzmann distribution through an artificial relaxation process. The standard way is to realize the Gibbs-Boltzmann distribution under the detailed balance condition. Recent progress on a technique proposed by Suwa and Todo makes it possible to accelerate the relaxation process, while avoiding the detailed balance condition. Since the dynamical stochastic system implemented to perform the Monte-Carlo simulation does not possess an equilibrium state but a steady state, we must design the steady state to be equivalent to the desired distribution such as the Gibbs-Boltzmann one. In other words, we then exploit nonequilibrium behavior with some current to accelerate the relaxation to the desired distribution. Several evidence in the previous studies exists but we do not have an answer to a simple question how the absence of the detailed balance condition accelerates the convergence to the desired distribution. In the present study, in order to address this problem, we find several relations in the nonequilibrium process without equilibrium but with steady state. By use of the obtained relations, we discuss the mechanism of the fast convergence in the case without the detailed balance condition.
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http://arxiv.org/abs/1307.0434
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