Dependence of dissipation on the initial distribution over states

TL;DR

This paper investigates how the initial state distribution influences work dissipation in nonequilibrium processes, revealing an information-theoretic measure that quantifies the excess dissipation beyond the minimal possible, applicable to computational systems.

Contribution

It introduces a simple information-theoretic function that quantifies the excess dissipation based on initial and final distributions, independent of process details, extending to computational systems.

Findings

The difference in dissipation is given by an information-theoretic function.

This difference is independent of the process specifics.

Results apply to coarse-grained macrostates in computational models.

Abstract

We analyze how the amount of work dissipated by a fixed nonequilibrium process depends on the initial distribution over states. Specifically, we compare the amount of dissipation when the process is used with some specified initial distribution to the minimal amount of dissipation possible for any initial distribution. We show that the difference between those two amounts of dissipation is given by a simple information-theoretic function that depends only on the initial and final state distributions. Crucially, this difference is independent of the details of the process relating those distributions. We then consider how dissipation depends on the initial distribution for a 'computer', i.e., a nonequilibrium process whose dynamics over coarse-grained macrostates implement some desired input-output map. We show that our results still apply when stated in terms of distributions over the computer's coarse-grained macrostates. This can be viewed as a novel thermodynamic cost of computation, reflecting changes in the distribution over inputs rather than the logical dynamics of the computation.