Thinking transport as a twist

TL;DR

This paper explores how the conductivity of classical systems connected to reservoirs can be understood through the concept of stiffness in a quantum-like operator, linking boundary coupling mechanics to transport properties.

Contribution

It introduces a novel mapping of classical transport problems to quantum-like stiffness calculations, highlighting the role of reservoir coupling in boundary torque mechanics.

Findings

Mapping classical conductivity to quantum-like stiffness.

Role of reservoir coupling in boundary torque mechanics.

Framework applicable to deterministic and stochastic systems.

Abstract

The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the `energy' cost of twisting the boundaries) of a quantum-like operator. The nature of the coupling to the reservoirs determines the details of the mechanical coupling of the torque at the ends.