Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information

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: 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 $n\times k_BT\ln2$ 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 Holevo-Schumacher-Westmoreland Theorem and a series of strong converse properties as well as no-go theorems.