Current large deviation function for the open asymmetric simple exclusion process

Introduction. One of the main open problems in classical statistical physics is the formulation and derivation of simple laws that determine macroscopic quantities in strongly interacting systems far from equilibrium. A broad class of nonequilibrium systems can be characterized by the presence of a macroscopic current. An important diagnostic tool of non-equilibrium behaviour is then provided by the probability distribution of current fluctuations. The latter is suitably represented in terms of its moments, which are encoded in the current large deviation function (LDF). LDFs play an important role in the application of fluctuation theorems [1–3]. Microscopic models of interacting particles provide a useful framework for studying non-equilibrium properties in current-carrying classical systems and have become a major subject of research over the past two decades. One of their main uses is that their large deviation properties can be derived microscopically, which furnishes rigorous tests of underlying assumptions in phenomenological approaches. The asymmetric simple exclusion process (ASEP), describing the asymmetric diffusion of hard-core particles along a one-dimensional chain, is one of the best studied paradigms of non-equilibrium Statistical Mechanics [4]. The ASEP is of general interest due to its close relation to growth phenomena [5], as observed in recent experiments on electroconvection [6]. It is also used as a model of molecular diffusion in zeolites [7], of biopolymers [8] and sequence alignment [9], traffic flow [10] and quantum dot chains [11]. The exact probability distribution for current fluctuations for the ASEP on a ring has been known for some time [12]. In the open boundary ASEP phenomenological [13], approximate [11] and numerical [14] treatments have been developed, but the determination of the current LDF from first principles has been one of the outstanding problems in the field. Despite considerable effort, the LDF is only known in the limiting cases of symmetric exclusion [15] and weak asymmetry [16]. For the infinite system the time dependence was obtained for total asymmetry in [17].