Systematic derivation of coarse-grained fluctuating hydrodynamic equations for many Brownian particles under nonequilibrium conditions

Einstein relation and hydrodynamics of nonequilibrium mass transport processes

We derive hydrodynamics of paradigmatic conserved-mass transport processes on a ring. The systems, governed by chipping, diffusion, and coalescence of masses, eventually reach a nonequilibrium steady state, having nontrivial correlations, with steady-state measures in most cases not known. In these processes, we analytically calculate two transport coefficients, bulk-diffusion coefficient and conductivity. Remarkably, the two transport coefficients obey an equilibrium-like Einstein relation even when the microscopic dynamics violates detailed balance and systems are far from equilibrium. Moreover, we show, using a macroscopic fluctuation theory, that the probability of large deviation in density, obtained from the above hydrodynamics, is in complete agreement with the same derived earlier by Das et al. [Phys. Rev. E 93, 062135 (2016)2470-004510.1103/PhysRevE.93.062135] using an additivity property.

Macroscopic expression connecting the rate of energy dissipation with the violation of the fluctuation response relation

A direct connection between the magnitude of the violation of the fluctuation response relation (FRR) and the rate of energy dissipation is presented in terms of field variables of nonequilibrium systems. Here, we consider the density field of a colloidal suspension either in a relaxation process or in a nonequilibrium steady state driven by an external field. Using a path-integral representation of the temporal evolution of the density field, we find an equality that relates the magnitude of the violation of the FRR for scalar and vector potentials of the velocity field to the rate of energy dissipation for the entire system. Our result demonstrates that the violation of the FRR for field variables captures the entropic component of the dissipated free energy.

The structural dynamics of macromolecular processes

Dynamic processes involving macromolecular complexes are essential to cell function. These processes take place over a wide variety of length scales from nanometers to micrometers, and over time scales from nanoseconds to minutes. As a result, information from a variety of different experimental and computational approaches is required. We review the relevant sources of information and introduce a framework for integrating the data to produce representations of dynamic processes.

Fluctuation-response relation of many Brownian particles under nonequilibrium conditions

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in nonequilibrium cases. This result suggests that Einstein's formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.