1306.6131 (Akihisa Ichiki et al.)

Violation of detailed balance accelerates relaxation    [PDF]

Akihisa Ichiki, Masayuki Ohzeki

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. From the viewpoint of stochastic quantization, although the convergence is accelerated by the introduction of asymmetry in the Hamiltonian of corresponding quantum systems, the achievable relaxation speed is bounded by the symmetric part of the Hamiltonian.

View original: http://arxiv.org/abs/1306.6131