Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

Abstract

We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions.

Comment on “Generalized exclusion processes: Transport coefficients”

“…The extrapolation to the d → ∞ limit is close to the uncorrelated result. The same 1/d scaling was found in [6]. As a further illustration, we plot D 2 (ρ) in one dimension in Figure 5 together with Eq.…”

Structure of the optimal path to a fluctuation

“…For that we fix the boundary densities to ρ(r, t)| x =0,1 = ρ 0,1 , which drive the system out of equilibrium as soon as ρ 0 = ρ 1 , setting periodic boundary conditions for all other directions of space. This class of systems has been broadly studied during the last years, finding that a simplifying conjecture within MFT known as (weak) Additivity Principle (AP) [56] allows to solve the problem of current statistics both for d = 1 [5,45,[49][50][51] and d > 1 [54][55][56][57]60]. The AP, which offers explicit expressions for the current LDF and the optimal paths supporting a given fluctuation, establishes that the most probable trajectory to a current fluctuation is time-independent (apart from some initial and final transients of negligible weight for the current LDF).…”

“…(11) imposes on the optimal current fields, it is important to realize that in all high-dimensional problems studied in literature up to now the dominant paths responsible of a current fluctuation, corresponding to the global extrema of the action I τ in Eq. (7), always exhibit structure (if any) along a principal direction, that we denote here as x [5,31,[54][55][56][57]. This means in particular that ρ q (r, t) = ρ q (x , t) and j q (r, t) = j q (x , t).…”

“…The complexity of the MFT variational problem is such that most studies to date have focused on the current statistics of oversimplified one-dimensional (1d) transport models for which the MFT problem is somewhat simpler, specially when aided with the Additivity Principle [45][46][47][48][49][50][51][52][53]. Only very recently MFT has been used to understand current fluctuations in more realistic highdimensional (d > 1) systems [5,31,39,[54][55][56][57], and these studies have unveiled a rich phenomenology which only appears for d > 1, including hidden symmetries leading to new fluctuation theorems [39], a weak generalization of the Additivity Principle [56], and complex dynamic phase transitions associated to competing emergent orders and symmetry breaking phenomena [31]. Crucially, the richness found in d > 1 stems in all cases from the relevance of structured optimal current fields at the fluctuating level, a common trait of all these new results [31,56,57].…”

Focus on stochastic thermodynamics

“…Experimental results for the work distribution of interacting colloidal particles forming a colloidal crystal that is driven across a commensurate periodic light field are presented by Gomez-Solano et al  [25]. Transport in interacting systems is studied by Becker et al for a boundary driven set-up, for which they show simulations that support predictions from macroscopic fluctuation theory and the additivity principle [26]. For a driven manyparticle system with zero-range interactions, Asban and Rahav derive an effective non-linear diffusion equation and discuss the applicability of the no-pumping theorem to such systems [27].…”