The Stochastic Thermodynamics of Communication

The thermodynamic cost of communication is a major contributor to the total thermodynamic cost of real-world computers, both biological (e.g., the brain) and digital. However, little is known about the fundamental features of this cost. Here, we analyze how the channel information capacity - a property of communication systems that is fundamental to modern information theory - is related to the entropy production in a communication channel. We focus on the specific case of the entropy production (EP) of a linear error-correcting code, in which an input message is encoded using the Hamming code; transmitted through a noisy channel; and then recovered with an associated decoder.

We represent the encoder as a periodic (clocked) XOR circuit. We calculate the mismatch cost lower bound on the EP of that encoder, which allows us to avoid precise modeling of its physical implementation. The binary channel is modeled as a 2-spin system in which the output is biased to equal the input, and the spin pair is in a nonequilibrium steady state. We consider several possible physical models of the decoder, including a novel model of it as a thermal relaxation process. A central concern of our analysis is the effect of varying the input distribution, which not only affects the thermodynamic costs of running the full encoder, channel, and decoder system but also influences the mutual information between inputs and outputs.