Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics

Abstract

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition-probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.

18pages, 3 figures, proceeedings of STATPHYS KOLKATA VIII

References in corpus (5)

• Markov Chain Monte Carlo Method without Detailed Balance
• Violation of detailed balance accelerates relaxation
• Quantum annealing with Jarzynski equality
• Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
• Fluctuation Theorems on Nishimori Line

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• Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
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• Steady state distributions of network of degenerate optical parametric oscillators in solving combinatorial optimization problems
• Upper bound inequality for calculation time in simulated annealing analogous to adiabatic theorem in quantum systems