  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.
