Thermodynamic derivation of the mutual information for discrete symmetric channels

The mutual information for the binary symmetric channel as well as for the discrete symmetric channel consisting of 4-input/output (I/O) symbols is explicitly calculated using the generalized second law of thermodynamics which was recently proposed by the first two authors. For equiprobable I/O the mutual information of the examined channels has a very simple thermodynamic form as a function of the internal energy of the channel. We prove that this simple form of the mutual information governs the class of discrete memoryless symmetric communication channels with equiprobable I/O symbols.