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We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-rang
We investigate the particle and heat transport in quantum junctions with the geometry of star graphs. The system is in a nonequilibrium steady state, characterized by the different temperatures and chemical potentials of the heat reservoirs connected
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the over
Jarzynskis nonequilibrium work relation can be understood as the realization of the (hidden) time-generator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical
We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum Yang-Baxter
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a reaction-diffusion system