  Modeling communication channels as thermal systems results in Hamiltonians
which are an explicit function of the temperature. The first two authors have
recently generalized the second thermodynamic law to encompass systems with
temperature-dependent energy levels, $dQ=TdS+<d\mathcal{E}/dT>dT$, where
{$<\cdot>$} denotes averaging over the Boltzmann distribution, recomputing the
mutual information and other main properties of the popular Gaussian channel.
Here 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. For
equiprobable I/O the mutual information of the examined channels has a very
simple form, -$\gamma U(\gamma)|_0^\beta$, where $U$ denotes 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.
