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 the following: 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>n</a:mi></a:math> bits of classical information <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>n</b:mi><b:mo>×</b:mo><b:msub><b:mi>k</b:mi><b:mi>B</b:mi></b:msub><b:mi>T</b:mi><b:mo form="prefix">ln</b:mo><b:mn>2</b:mn></b:mrow></b:math> transmitted energy. Unexpectedly, these bounds further uncover a dynamical version of Landauer's principle, showing the strong link between (rather than ) 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.