How Dissipation Constrains Fluctuations in Nonequilibrium Liquids: Diffusion, Structure, and Biased Interactions

Abstract

The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials. arXiv:1808.07838v4 [cond-mat.stat-mech]

Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles

“…Note that our derivation does not rely on any response theory at variance with recent works [65][66][67]. Moreover, we consider here that both the tracer and its surrounding particles are active, in contrast with [36] which only considered a dilute fraction of active tracers in a bath of passive particles, and the tracer statistics can now be derived for an arbitrary strength of the active force.…”

“…It takes values between 0 and 1, respectively in the absence of interactions and when all particles are in stable clusters. Besides, it is proportional to the 'rate of work' introduced recently in nonequilibrium liquids as a measure of the drive-induced dynamical and structural changes [36,55]. With this definition, the efficiency is small when most of the dissipation is due to free motion and the fluid only features a small number of clusters, whereas the efficiency is large when particles dissipate less power in the solvent by forming large clusters.…”

“…To this aim, we rely on the fact that the active fluctuations of the self-propulsion can be mapped into a deterministic drive with disordered amplitude. Following a recent work [36], we introduce a set of driving forces f i describing periodic orbits in the reference frame of each particle as…”

“…The reduction of transport coefficients by activity is then often regarded as a precursor of cluster formation. While several works have strived to predict how internal transport is affected by activity [30][31][32][33][34][35], a recent study has put forward an explicit connection between diffusion and dissipation in a mixture of active and passive particles [36]. Moreover, for generic driven systems, it has been shown recently that the diffusion coefficient is generically bounded by dissipation [37][38][39][40][41].…”

“…In section 2, we introduce the collisional efficiency to quantify cluster formation in terms of energy transfers between the particles and their environment. To predict how this efficiency behaves in terms of microscopic details, we build on the mapping of active particles into driven particles proposed in [36]. It consists in describing the random self-propulsion as a disordered drive, which allows us to coarse-grain the active dynamics using methods of driven fluids, as detailed in section 3.…”