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We consider networks made of parallel lanes along which particles hop according to driven diffusive dynamics. The particles also hop transversely from lane to lane, hence indirectly coupling their longitudinal dynamics. We present a general method for constructing the phase diagram of these systems which reveals that in many cases their physics reduce to that of single-lane systems. The reduction to an effective single-lane description legitimizes, for instance, the use of a single TASEP to model the hopping of molecular motors along the many tracks of a single microtubule. Then, we show how, in quasi-2D settings, new phenomena emerge due to the presence of non-zero transverse currents, leading, for instance, to strong `shear localisation along the network.
We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagra
When an extended system is coupled at its opposite boundaries to two reservoirs at different temperatures or chemical potentials, it cannot achieve a global thermal equilibrium and is instead driven to a set of current-carrying nonequilibrium states.
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of mic
Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete exposition, the d
We study the behavior of stationary non-equilibrium two-body correlation functions for Diffusive Systems with equilibrium reference states (DSe). A DSe is described at the mesoscopic level by $M$ locally conserved continuum fields that evolve through