Nonequilibrium ensemble inequivalence and large deviations of the density in theABCmodel

Abstract

We consider the one-dimensional driven ABC model under particle-conserving and particle-nonconserving processes. Two limiting cases are studied: (a) The rates of the nonconserving processes are vanishingly slow compared with the conserving processes in the thermodynamic limit and (b) the two rates are comparable. For case (a) we provide a detailed analysis of the phase diagram and the large deviations function of the overall density, G(r). The phase diagram of the nonconserving model, derived from G(r), is found to be different from the conserving one. This difference, which stems from the nonconvexity of G(r), is analogous to ensemble inequivalence found in equilibrium systems with long-range interactions. An outline of the analysis of case (a) was given in an earlier letter. For case (b) we show that, unlike the conserving model, the nonconserving model exhibits a moving density profile in the steady state with a velocity that remains finite in the thermodynamic limit. Moreover, in contrast with case (a), the critical lines of the conserving and nonconserving models do not coincide. These are new features which are present only when the rates of the conserving and nonconserving processes are comparable. In addition, we analyze G(r) in case (b) using macroscopic fluctuations theory. Much of the derivation presented in this paper is applicable to any driven-diffusive system coupled to an external particle bath via a slow dynamics.

Dynamical phase transitions in one-dimensional hard-particle systems

“…We now consider the constant-pressure version of the model, in which the system size evolves in time according to equation (5). In equilibrium, one expects local properties of single phases to be independent of ensemble.…”

“…Out-of-equilibrium systems differ from their equilibrium counterparts in many ways. For example, longranged correlations are generic in non-equilibrium steady states [1,2]; unusual phase transitions can take place [3]; and there may be significant differences in behavior for the same system in different ensembles (for example, canonical and grand canonical [4,5]). Recently, there has been considerable interest in large-deviation phenomena [6], based on ensembles of trajectories that are conditioned on atypical values of time-averaged observables [7][8][9][10].…”

Relaxation processes in a system with logarithmic growth

“…Anomalous coarsening with logarithmic domain growth has been identified in a variety of situations with dynamical constraints, as for example in the ABC model introduced by Evans et al [26,27], where three different particle types swap places asymmetrically, in the model discussed by Lahiri and Ramaswamy [28,29], where two sublattices are considered with two types of particles on each sublattice, or in the driven two-lane particle system studied by Lipowski and Lipowska [30]. Among these models, the one-dimensional ABC model has enjoyed much attention in recent years [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], due to its unique properties combined with its amenability to exact calculations in some special cases. Thus the ABC model provides an opportunity to study exactly the long-range correlations in a system undergoing a non-equilibrium phase transition as well as to elucidate ensemble inequivalence far from equilibrium.…”

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

“…The inequivalence of different ensembles in the Blume-Emery-Griffiths model has been reported earlier in [12,22] in the absence of magnetic field. In the (T − ∆) plane, while the λ line equation is same in both the ensembles, the first order line and the multicritical points are known to be located differently [36][37][38][39]. It was reported that the TCP and other multicritical points are different for canonical and microcanonical ensembles for a given value of K [12,22].…”