Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics

Abstract

Energy transfer and information transmission are two fundamental aspects of nature. They are seemingly unrelated, while recent findings suggest that a deep connection between them is to be discovered. This amounts to asking: Can we phrase the processes of transmitting classical bits equivalently as specific energy-transmitting tasks, thereby uncovering foundational links between them? We answer this question positively by showing that, for a broad class of classical communication tasks, a quantum dynamics' ability to transmit $n$ bits of classical information is equivalent to its ability to transmit $n$ units of energy in a thermodynamic task. This finding not only provides an analytical correspondence between information transmission and energy extraction tasks, but also quantifies classical communication by thermodynamics. Furthermore, our findings uncover the dynamical version of Landauer's principle, showing the strong link between transmitting information and energy. In the asymptotic regime, our results further provide thermodynamic meanings for the well-known Holevo-Schumacher-Westmoreland Theorem in quantum communication theory.

5+3 pages, 3 figures, closed to published version

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• Active energy harvesting and work transduction by hair-cell bundles in bullfrog's inner ear
• Thermodynamic criteria for signaling in quantum channels
• Complete characterisation of state conversions by work extraction
• General quantum resources providing advantages in work-extraction tasks
• Improving the efficiency of finite-time memory erasure with potential barrier shaping
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles