Landauer Principle and the Second Law in a Relativistic Communication Scenario

TL;DR

This paper explores how thermodynamics and information theory interact in a relativistic communication scenario, using Landauer's principle and the second law.

Contribution

The novel contribution is deriving a bound on energy expenditure for information acquisition in relativistic spacetime.

Findings

A bound on energy expenditure for information acquisition is derived based on spacetime metric and channel properties.

Landauer’s principle and the second law are applied to constrain work extraction in relativistic communication.

The study connects thermodynamics with relativistic information transfer through a heat engine model.

Abstract

The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical nature of information, which underpins Landauer’s principle, we believe that information theory should play a role in understanding this problem. In this work, we contribute to this endeavour by considering a relativistic communication task between two partners, Alice and Bob, in a general Lorentzian spacetime. We then assume that the receiver, Bob, reversibly operates a local heat engine powered by information, and seek to determine the maximum amount of work he can extract from this device. As Bob cannot extract work for free, by applying both Landauer’s principle and the second law of thermodynamics, we establish a bound on the energy Bob must spend to acquire the information in the first place. This bound is a function of the spacetime metric and the properties of the communication channel.