LMP Seminar: Effective dynamics of rare-events in non-equilibrium dynamical systems

Recently much attention has been devoted to conditioning a Markov process on a rare event of a large deviation-type system. This means fixing the value of a given dynamical observable on an atypical value. On the other hand, there is a conditioning-free process, known as the effective or driven process, in which this atypical value becomes typical. we first studied fluctuations of dynamical observables in some exclusion single-species reaction-diffusion model with nearest-neighbor interactions on a one-dimensional lattice with periodic boundary conditions. We have found certain constraints on the microscopic transition rates of the process under which the effective process contains local interactions. On the other hand, A totally asymmetric exclusion process consisting of classical particles with next-nearest-neighbor interactions has been considered on a 1D discrete lattice with a ring geometry. Using large deviation techniques, we have investigated fluctuations of particle current in two and three-particle sectors. In two-particle sector, we have found that the phase diagram of the process has three different phases in each of which the dynamical free energy of the system behaves differently. Calculating the effective potential for a given configuration allows us to find the propensity or natural tendency of that configuration to exhibit flux in the future. We have also been able to find those configurations which generate high particle current in each phase.