Eur. Phys. J. B (2021) 94: 145
https://doi.org/10.1140/epjb/s10051-021-00164-1

Topical Review - Statistical and Nonlinear Physics

A large deviation theory perspective on nanoscale transport phenomena

¹ Department of Chemistry, University of California, 94609, Berkeley, CA, USA
² Kavli Energy NanoScience Institute, 94609, Berkeley, CA, USA
³ Materials Science Division, Lawrence Berkeley National Laboratory, 94609, Berkeley, CA, USA
⁴ Chemical Science Division, Lawrence Berkeley National Laboratory, 94609, Berkeley, CA, USA

^a dlimmer@berkeley.edu

Received: 12 April 2021
Accepted: 13 July 2021
Published online: 20 July 2021

Abstract

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low-dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium steady states and relating those fluctuations to nonlinear or anomalous responses. We have developed a systematic framework for computing distributions of time integrated currents in molecular models and relating cumulants of those distributions to nonlinear transport coefficients. The approach elaborated upon in this perspective follows from the theory of dynamical large deviations, benefits from substantial previous formal development, and has been illustrated in several applications. The framework provides a microscopic basis for going beyond traditional hydrodynamics in instances where local equilibrium assumptions break down, which are ubiquitous at the nanoscale.