Effective dynamics in an asymmetric death-branching process
arXiv:1906.08630 · doi:10.1088/1742-5468/aa82c7
Abstract
In this paper we study activity fluctuations in an asymmetric death-branching process in one-dimension. The model, which is a variant of the asymmetric Glauber model, has already been studied in [12]. It is known that in the low-activity region i.e. below the typical activity in the steady-state, the dynamical free energy of the system can be calculated exactly. However, the behavior of the system in the high-activity region is different and more interesting. The system undergoes a series of dynamical phase transitions. In present work we justify the hierarchy of dynamical phase transitions in terms of effective interactions in the system. It turns out that the effective interactions are long-range and that they can be described in terms of interactions between repelling shock fronts.
arXiv comment15 pages, 3 eps figure, accepted for publication in JSTAT
References in corpus (14)
- The large deviation approach to statistical mechanics
- Fluctuation theorems for stochastic dynamics
- 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
- Effective interactions and large deviations in stochastic processes
- Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux
- Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
- Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
- Phase transition in an asymmetric generalization of the zero-temperature Glauber model
- On Effective Stochastic Generators for Conditioned Dynamics at an Atypical Reaction-Diffusion Current
- Particle current fluctuations in a variant of asymmetric Glauber model
- Rare-event trajectory ensemble approach to study dynamical phase transitions in the zero temperature Glauber model