Einstein relation and hydrodynamics of nonequilibrium mass transport processes

Exact closure and solution for spatial correlations in single-file diffusion

In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.

Transport and fluctuations in mass aggregation processes: Mobility-driven clustering

We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)10.1103/PhysRevLett.81.3691] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.

Hard core run and tumble particles on a one-dimensional lattice

We study the large scale behavior of a collection of hard core run and tumble particles on a one-dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady-state single-site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence-fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the nongradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

Additivity and density fluctuations in Vicsek-like models of self-propelled particles

We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation-the direct consequence of an additivity property-we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide evidence of the existence of an equilibriumlike chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.

Hydrodynamics, density fluctuations, and universality in conserved stochastic sandpiles

We study conserved stochastic sandpiles (CSSs), which exhibit an active-absorbing phase transition upon tuning density ρ. We demonstrate that a broad class of CSSs possesses a remarkable hydrodynamic structure: There is an Einstein relation σ^{2}(ρ)=χ(ρ)/D(ρ), which connects bulk-diffusion coefficient D(ρ), conductivity χ(ρ), and mass fluctuation, or scaled variance of subsystem mass, σ^{2}(ρ). Consequently, density large-deviations are governed by an equilibrium-like chemical potential μ(ρ)∼lna(ρ), where a(ρ) is the activity in the system. By using the above hydrodynamics, we derive two scaling relations: As Δ=(ρ-ρ_{c})→0^{+}, ρ_{c} being the critical density, (i) the mass fluctuation σ^{2}(ρ)∼Δ^{1-δ} with δ=0 and (ii) the dynamical exponent z=2+(β-1)/ν_{⊥}, expressed in terms of two static exponents β and ν_{⊥} for activity a(ρ)∼Δ^{β} and correlation length ξ∼Δ^{-ν_{⊥}}, respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality-not that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).