Dynamical Landauer Principle

Chung-Yun Hsieh^1*

¹School of Physics, University of Bristol, Bristol, UK

* Presenter:Chung-Yun Hsieh, email:chung-yun.hsieh@bristol.ac.uk

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 thus motivates us to ask the following question:

Can information transmission tasks equal certain energy transmission tasks?

More precisely, can we phrase the processes of transmitting classical bits equivalently as some energy-transmitting tasks, thereby uncovering foundational links between them? A suitable answer can bridge quantum communication and thermodynamics. In this work, we answer this question positively by showing that:

A quantum channel’s ability to transmit n bits of information is equivalent to its ability to transmit n×kT ln2 amounts of (work-like) energy.

Here, k is the Boltzmann constant, and T is a background temperature. More formally, this is proved by bounding various types of one-shot classical capacities [1] by different energy transmission tasks introduced in this work. This finding not only provides a correspondence between information transmission and energy transfer, but also quantifies classical communication by thermodynamics. Interestingly, in the asymptotic regime, this result further provides a thermodynamic form of the well-known Holevo-Schumacher-Westmoreland theorem [2-4] in quantum communication.

Crucially, the equivalence between the abilities to do two things may not directly imply that these two things are equivalent. Using the tasks introduced here, we argue that transmitting information and energy can happen simultaneously via the same physical process (described by a quantum channel). This thus enables us to uncover a truly work-like dynamical version of Landauer’s principle [5]. We present a physical setting (combining tasks of communication and energy transmission) to argue that:

In the presented setting, if a quantum channel is transmitting n bits of information, it must also transmit at least n×kT ln2 amounts of (work-like) energy.

Just like the profound Landauer’s principle uses the physical setting of erasure processes to uncover the necessary energetic criterion of erasing information [5], we uncover the necessary energetic criterion of transmitting (rather than erasing) information, in a setting that is fully operational and experimentally feasible. This new notion of Landauer’s principle reveals the strong link between transmitting information and energy, which can potentially bridge communication and thermodynamics with both foundational and practical impacts.

This submission covers results from Refs. [6,7].

References
[1] L. Wang and R. Renner, One-shot classical-quantum capacity and hypothesis testing, Phys. Rev. Lett. 108, 200501 (2012).
[2] A. S. Holevo, Bounds for the quantity of information transmitted by a quantum communication channel, Prob. Peredachi Inf. 9, 3 (1973).
[3] A. S. Holevo, The capacity of the quantum channel with general signal states, IEEE Trans. Inf. Theory 44, 269 (1998).
[4] B. Schumacher and M. D. Westmoreland, Sending classical information via noisy quantum channels, Phys. Rev. A 56, 131 (1997).
[5] R. Landauer, Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 5, 183 (1961).
[6] C.-Y. Hsieh, Dynamical Landauer principle: Quantifying information transmission by thermodynamics, Phys. Rev. Lett. 134, 050404 (2025).
[7] C.-Y. Hsieh, Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information, Phys. Rev. A 111, 022207 (2025).

Keywords: Quantum communication, Quantum thermodynamics, Informational thermodynamics, Quantum resource theories, Landauer's principle