Minimal thermodynamic cost of communication

Abstract: Thermodynamic cost of communication is a major factor in the thermodynamic cost of real-world computers, both biological and digital. Despite its importance, the fundamental principles underlying this cost remain poorly understood. This paper makes two major contributions to addressing this gap. First, we derive a universal relationship between information transmission rate and minimal entropy production (EP) by focusing on the mismatch cost (MMC) component of thermodynamic cost. The resulting relationship holds independently of the underlying physical dynamics, making it broadly applicable. We discuss the implications of the derived minimal communication cost for work extraction in measurement-and-feedback protocols, and through examples involving binary channels, we show that the relationship between transmission rate and minimal thermodynamic cost can exhibit diminishing returns in certain scenarios. Second, we extend this thermodynamic analysis to the computational front and back ends critical to communication-namely, encoding and decoding to reduce errors in noisy transmission. Using the framework of periodic machines, we establish strictly positive minimal costs for implementing linear error-correcting codes. We compare these costs with end-to-end error rates, highlighting trade-offs between thermodynamic cost and decoding accuracy.