The exponential distribution in information theory

The exponential distribution is shown to lead to theory-information formulas which are very similar to their analogs in the Gaussian case. These formulas are ones for mutual information between a random value and its sum with exponentially distributed value, when the saddle point property is satisfied, velocity as distortion function for Poisson process, capacity of a channel with one user and a channel of multiple access with additive exponential noise as well as for capacity of controlled Markov processes.