Molecular Insight into Nonlinear Transport Behaviors

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to compute arbitrarily high order transport coefficients of stochastic systems, using the framework of large deviation theory. Leveraging time reversibility in the microscopic dynamics, we relate nonlinear response to equilibrium multi-time correlation functions among both time reversal symmetric and asymmetric observables, which can be evaluated from derivatives of large deviation functions. This connection establishes a thermodynamic-like relation for nonequilibrium response and provides a practical route to its evaluation, as large deviation functions are amenable to importance sampling. Two important features of this new method are highlighted in this work. Firstly, its efficiency is demonstrated by comparison with direct nonequilibrium simulations, the Green-Kubo method, and brute-force evaluations of the higher order correlation functions. Secondly, its utility in generating molecular insight is showcased in a couple of examples, including the field-dependent conductivities in electrolyte solutions, and thermal rectification in nonlinear lattices. In addition to the methodology development, we also explore how molecular insight into nonlinear transport behaviors can provide us with design principles for nanoscale devices. This is done by introducing a thermodynamically consistent, minimal stochastic model for complementary logic gates built with field-effect transistors. We characterize the performance of such gates with tools from information theory and study the interplay between accuracy, speed, and dissipation of computations. This work provides a platform to study design principles for low dissipation computing devices harnessing the theoretical developments in stochastic thermodynamics