# Einstein relation and hydrodynamics of nonequilibrium mass transport processes

## TL;DR

This paper derives hydrodynamic equations for a class of nonequilibrium mass transport processes, calculates key transport coefficients, and finds an Einstein relation despite the absence of detailed balance.

## Contribution

It provides analytical expressions for diffusion and conductivity in nonequilibrium systems and reveals an Einstein relation similar to equilibrium, despite complex microscopic dynamics.

## Key findings

- Calculated bulk-diffusion coefficient and conductivity.
- Established Einstein relation holds in nonequilibrium steady states.
- Confirmed fluctuation probabilities match previous theoretical predictions.

## Abstract

We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their nonequilibrium steady states, having nontrivial correlations, are not known. In these processes, we analytically calculate two transport coefficients, the bulk-diffusion coefficient and the conductivity. We, remarkably, find that the two transport coefficients obey an equilibriumlike Einstein relation, although the microscopic dynamics does not satisfy detailed balance condition. Using macroscopic fluctuation theory, we also show that probability of density fluctuations obtained from the hydrodynamic description is in complete agreement with the same derived earlier in [Phys. Rev. E 93, 062135 (2016)] using an additivity property.