The second law of thermodynamics for communication channels

The classical thermodynamic laws fail to capture the behavior of systems with energy Hamiltonian being an explicit function of the temperature. Such Hamiltonian arises, for example, in modeling information processing systems, like communication channels, as thermal systems. Here we generalize the second thermodynamic law to encompass systems with temperature-dependent energy levels, dQ = TdS+ < d¿/dT > dT , where < · > denotes averaging over the Boltzmann distribution. It enables to quantitatively bridge between the realm of thermodynamics and information theory in the context of communication channels. In particular, this generalization enables to express information measures (e.g., mutual information) of the popular Gaussian and binary-symmetric channels as a direct consequence of the laws of nature - the laws of thermodynamics.