Communication, Dynamical Resource Theory, and Thermodynamics

TL;DR

This paper explores how dynamical resources influence classical communication and thermodynamics, revealing bounds on capacity, thermodynamic costs, and new ways to transmit information using thermalization and classical correlations.

Contribution

It introduces bounds on classical capacity based on resource preservability, links bath size to thermodynamic costs, and demonstrates communication via thermalization using classical correlations.

Findings

One-shot classical capacity is bounded by resource preservability.

Bath size bounds the thermodynamic cost of communication.

Classical correlations enable communication even in thermalized systems.

Abstract

Recently, new insights have been obtained by jointly studying communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we analyze the role of dynamical resources in a communication setup, and further apply our analysis to thermodynamics. To start with, we study classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. We show that the one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its one-shot classical capacity. When the channel is coherence non-generating, the upper bound is given by a sum of coherence preservability and the bath size of the channel's incoherent version. In this sense, bath sizes can be interpreted as the thermodynamic cost of transmitting classical information. This finding provides a dynamical analogue of Landauer's principle, and therefore bridges classical communication and thermodynamics. As another implication, we show that, in bipartite settings, classically correlated local baths can admit classical communication even when both local systems are completely thermalized. Hence, thermalizations can transmit information by accessing only classical correlation as a resource. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.