Fluctuation-Induced Forces in Nonequilibrium Diffusive Dynamics

Abstract

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 ...

Nonequilibrium forces following quenches in active and thermal matter

“…The solid black curve shows Eq. (22). At low temperatures, the particles are trapped between the two inclusions which become more and more like impenetrable "plates," so that the curve approaches the shape of the curve in Fig.…”

“…(22) at high T F as expected, with the only visible deviation for long times, were the simulation data approach zero faster than expected from Eq. (22). The finite size of the simulation box cuts off the power-law decay in time; see Appendix C. In contrast to the 2D case, the PQF is qualitatively different for low T F , where it tends to the result of Sec.…”

“…Indeed, in the presence of conserved quantities (such as density), systems out of equilibrium generically display long-ranged correlations [16][17][18]. Associated FIFs have been studied theoretically in driven steady states such as fluids subject to temperature gradients [19][20][21], particles diffusing in a density gradient [22], and in shaken granular systems [23][24][25]. Rather than driven states, Ref.…”

Nonequilibrium Casimir-like Forces in Liquid Mixtures

“…negative, essentially depending on whether the concentration dependence of the heat of mixing is convex or concave. Some authors have proposed NE Casimir forces induced by long-range fluctuations that originate from the spatial dependence of the noise correlations associated with the local fluctuation-dissipation theorem in the presence of a gradient [36,37]. However, for fluids it has been found that these NE correlations are insignificant compared to the NE correlations caused by a coupling between hydrodynamic modes in NE states considered here [38].…”

A Review on Polymer Crystallization Theories

“…Nevertheless, for non-equilibrium systems along with strong correlations, it is uncertain whether scaling arguments could be valid. Recent studies on non-equilibrium systems [188] found that, even under far from equilibrium conditions, unexpected long-range correlations may appear. Power-law behaviors indicate the potential application of scaling analysis; such a treatment, however, has seldom appeared in the literature.…”