Some Analogies Between Thermodynamics and Shannon Theory

In this paper we present some analogies between thermodynamics and certain Shannon theory results. We revisit the previously published results that relate notion of energy and information. We then introduce a thermodynamic system that could be used to store information. The ideal gas is considered. We present the corresponding thermodynamic analysis and establish equivalence with the additive white Gaussian noise (AWGN) channel capacity formula. Specifically, we show that the average energy needed for adiabatic compression of the ideal gas to 1/N of its initial volume is the same as the average energy needed to achieve the capacity C = log, N of the equivalent AWGN channel. In addition, the analysis is extended to show a link between the gas volume and minimum squared codeword distance. Furthermore, we show that the ideal gas which went through the adiabatic compression, and later settled according to the second law of thermodynamics, will reach an equilibrium state which is directly related to Shannon random coding and joint typicality decoding.