Nonequilibrium uncertainty principle from information geometry

TL;DR

This paper introduces a geometric uncertainty relation for nonequilibrium processes, linking the statistical distance traveled to entropy production and dissipation, with implications for memory erasure and state space analysis.

Contribution

It derives a classical uncertainty relation based on information geometry for nonequilibrium processes, providing bounds on entropy production and flow rates.

Findings

Expediting erasure increases dissipated heat and geometric uncertainty.

High-uncertainty initial conditions can be near equilibrium but still dissipative.

The geometric uncertainty bounds are independent of the shortest distance to equilibrium.

Abstract

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we define is an upper bound for the entropy production and flow rates, but it does not necessarily correlate with the shortest distance to equilibrium. For a model one-bit memory device, we find that expediting the erasure protocol increases the maximum dissipated heat and geometric uncertainty. A driven version of Onsager's three-state model shows that a set of dissipative, high-uncertainty initial conditions, some of which are near equilibrium, scar the state space.