  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 endeavor 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. Since 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.
