In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple channels. A common hypothesis is that such inverse multiplexing strategies reduce total thermodynamic costs. So far, however, there have been no physics-based results supporting this hypothesis. This gap existed partially because we have lacked a theoretical framework that addresses the interplay of thermodynamics and information in off-equilibrium systems. Here we present the first study that rigorously combines such a framework, stochastic thermodynamics, with Shannon information theory. We develop a minimal model that captures the fundamental features common to a wide variety of communication systems, and study the relationship between the entropy production of the communication process and the channel capacity, the canonical measure of the communication capability of a channel. In contrast to what is assumed in previous works not based on first principles, we show that the entropy production is not always a convex and monotonically increasing function of the channel capacity. However, those two properties are recovered for sufficiently high channel capacity. These results clarify when and how to split a single communication stream across multiple channels.

15 pages, 3 figures