Curl flux induced drift in stochastic differential equations in the zero-mass limit

Jinhua Wang and Bo Yuan

Physica A: Statistical Mechanics and its Applications, 2016, vol. 462, issue C, 898-911

Abstract: We consider the nonlinear stochastic dynamics of dissipative Hamiltonian systems with state-dependent friction and diffusion connected by the fluctuation–dissipation relation in high dimensions. The system under study has a close connection to Ao’s framework in constructing a dynamical potential for non-equilibrium processes without detailed balance. We study the limiting case where the mass approaches zero and give a new and complete derivation of effective stochastic differential equations. Using the Ito stochastic integral convention, we show that the limiting effective Langevin equations have a new drift term. This extra term happens to be identical to the corresponding anti-Ito (or isothermal) integral (requiring constant temperature) in one dimension. We, however, cannot obtain this additional drift term using conventional stochastic integrals in high dimension. It is interesting to note that in a high-dimensional system, a curl flux induced drift may appear even if the diffusion matrix is constant. Our findings are supported by numerical simulations. We further analyze and discuss the role of this new drift term in calculating the classic escape time. For the first time, to our knowledge, the relation between the escape rate and the anti-Ito integral is presented. We also demonstrate that the derived diffusion equations give a new sampling algorithm which can increase convergence speed in a simple two-dimensional example.

Keywords: Non-equilibrium processes; Stochastic integral; Non-detailed balance; Zero-mass limit; Escape time; Langevin sampling (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:462:y:2016:i:c:p:898-911

DOI: 10.1016/j.physa.2016.06.023

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