Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information

Abstract

Transmitting energy and information are two essential aspects of nature. Recent findings suggest they are closely related, while a quantitative equivalence between them is still unknown. This thus motivates us to ask the following: Can information transmission tasks equal certain energy transmission tasks We answer this question positively by bounding various one-shot classical capacities via different energy transmission tasks. Such bounds provide the physical implication that in the one-shot regime, transmitting n bits of classical information is equivalent to n×kBTln2 transmitted energy. Unexpectedly, these bounds further uncover a dynamical version of Landauer's principle, showing the strong link between transmitting (rather than erasing) information and energy. Finally, in the asymptotic regime, our findings further provide thermodynamic meanings for the Holevo-Schumacher-Westmoreland Theorem and a series of strong converse properties as well as no-go theorems.