A thermodynamic-like approach for the study of probabilistic systems

This paper starts by considering an arbitrary system for which the probability distribution P:={P1,P2,…,PN} of a measurable property, with N possible independent results, is known. By using the Hartley information (pseudo-energy), the escort probabilities of P and its Shannon entropy, a thermodynamic-like formalism is developed, including the deduction of the fundamental equation for the mean value of the pseudo-energies. Thus, the method allows a macrodescription of the system that is based on a purely mathematical procedure and involves thermodynamic-like variables. As a specific example we consider a bank that measures customer satisfaction by doing a statistical survey (satisfied or unsatisfied customers).