Fluctuations in nonequilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations, in turn, experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. Our model calculations show that the force falls off with slab separation d as k B T=d (at temperature T, and in all spatial dimensions) but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is nonuniversal and explicitly depends on dynamics. The techniques introduced can be used to study pressure and fluctuation induced forces in a broad class of nonequilibrium systems. [7,8], and liquid-vapor coexistences [9]. In both cases, quantum and classical, the underlying fluctuations are long-range correlated leading to forces that fall off as power laws. In the latter (for example, in an oil-water mixture), this is achieved by tuning to a critical point, while the former is a consequence of the massless nature of the photon field. Generically, in a fluid in equilibrium, correlations (and, hence, FIF) decay exponentially and are insignificant beyond a correlation length.Nonequilibrium situations provide another route to longrange correlated fluctuations: Systems which, in equilibrium, have zero or short-ranged correlations [C eq ∼ δ s ðxÞ in s dimensions], quite generically exhibit power law correlations (C neq ∼ 1=jxj α ) with conserved dynamics when out of equilibrium [10][11][12]. Thus, it is natural to inquire about the nature (strength and range) of FIF in corresponding nonequilibrium settings (where there is no matching force in equilibrium). Indeed, such forces have been explored in a number of circumstances, including driven granular fluids [13][14][15][16], shear flow [17], active matter systems [18], and in ordinary fluids due to the Soret effect [19] or subject to a temperature gradient [20,21]. However, despite these studies, they are much less understood than other FIF.Here, we explore FIF in diffusive systems which are far from thermal equilibrium. First, we consider, in detail, possibly the simplest (and, hence, analytically tractable) example of FIF in a system of diffusing particles which are subject only to hard core exclusion. The model is commonly referred to as the symmetric simple exclusion process (SSEP) [22]. Then, we present perturbative results for general diffusive systems. The methods introduced can be used to investigate a large variety of models.The setups examined are as follows: (a) The two dimensional system shown in Fig. 1(a); infinite in the y direction and connected to two reservoirs at x ¼ 0 and x ¼ L, with densities ρð0; yÞ ¼ ρ l and ρðL; yÞ ¼ ρ r , respectively. Two slabs, a distance d from each other, span the system along the x direction. (b) The three dimensional extension of this setup is depicted in Fig. 1(b), with the two slabs replaced by a tube of square cross section. (c) A generalized setup in which the slabs (or tube in three ...

Abstract. The large deviation functional of the density field in the weakly asymmetric simple exclusion process with open boundaries is studied using a combination of numerical and analytical methods. For appropriate boundary conditions and bulk drives the functional becomes non-differentiable. This happens at configurations where instead of a single history, several distinct histories of equal weight dominate their dynamical evolution. As we show, the structure of the singularities can be rather rich. We identify numerically analogues in configuration space of first order phase transition lines ending at a critical point and analogues of tricritical points. First order lines terminating at a critical point appear when there are configurations whose dynamical evolution is controlled by two distinct histories with equal weight. Tricritical point analogues emerge when there are configurations whose dynamical evolution is controlled by three distinct histories with equal weight. A numerical analysis suggests that the structure of the singularities can be described by a Landau like theory. Finally, in the limit of an infinite bulk bias we identify singularities which arise from a competition of s histories, with s arbitrary. In this case we show that all the singularities can be described by a Landau like theory.Singularities in Large Deviation Functionals of Bulk-Driven Transport Models 2

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