Effective Stochastic Generator with Site-dependent Interactions
arXiv:1710.10424 · doi:10.1063/1.5010335
Abstract
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper we investigate this possibility by considering systems of classical particles moving on a one-dimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process or there can be arbitrary many particles at single site as in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of unconditioned process can be local but site-dependent. As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above mentioned constraints.
arXiv commentAccepted for publication in Journal of Mathematical Physics
References in corpus (10)
- The large deviation approach to statistical mechanics
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
- Thermodynamic formalism for systems with Markov dynamics
- Nonequilibrium Markov processes conditioned on large deviations
- Large deviations and ensembles of trajectories in stochastic models
- Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
- Microscopic structure of shocks and antishocks in the ASEP conditioned on low current
- On Effective Stochastic Generators for Conditioned Dynamics at an Atypical Reaction-Diffusion Current
- Particle current fluctuations in a variant of asymmetric Glauber model