Minimal Thermodynamic Cost of Communicaiton

Heat generation in computation is an emerging focus in stochastic thermodynamics. However, despite being integral to computational systems, the thermodynamic cost of communication remains underexplored. Here, we provide a strictly positive lower bound on the unavoidable entropy production (EP) in any physical system implementing a communication channel. Specifically, we derive a relationship between the information transmission rate and the minimal EP required for that transmission. Using this, we show that transmitting information through multiple high-noise channels can, under certain conditions, be more thermodynamically efficient than a single low-noise channel.

Additionally, we examine the EP in the computational front-ends and back-ends of communication channels, focusing on encoding and decoding algorithms for error-correcting codes—key components of modern communication. We derive a lower bound on the EP required for any physical system implementing these algorithms and compare EP across different linear codes and error rates. Like the second law, these bounds are independent of the system's physical details, offering insights into the interplay between algorithmic design of error-correcting codes and thermodynamic efficiency.