We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbours, with a rate that depends on the occupation of all the neighbouring sites within a range R. This finite range process (FRP) for R = 0 reduces to the well known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of cluster-weight function of (R + 1) occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.

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Abstract. We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss possibility of condensation there.Keywords: Zero-range processes, Non-equilibrium processes, Exact results Zero range and finite range processes with asymmetric rate functions 2

Driven particles in the presence of crowded environment, obstacles, or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. Based on the empirical studies of conserved lattice gas model, two species exclusion model and other interacting particle systems we propose a new mechanism for complex many-particle systems where slowing down of certain non-driven degrees of freedom by the external field can give rise to NDM. To prove that the slowing down of the non-driven degrees is indeed the underlying cause, we consider several driven diffusive systems including two species exclusion models, misanthrope process, and show from the exact steady state results that NDM indeed appears when some non-driven modes are slowed down deliberately. For clarity, we also provide a simple pedagogical example of two interacting random walkers on a ring which conforms to the proposed scenario.