Disequilibrium, thermodynamic relations, and Rényi's entropy

The disequilibrium concept (D) was introduced by López-Ruiz, Mancini, and Calbet 20 years ago together with their successful notion of statistical complexity. In this note we show that, in a classical, canonical-ensemble environment, D displays interesting thermodynamic properties and is able to replace the partition function. Also, we show that for a generalized Statistical Complexity-family that involves Rényi's entropy of order q, the maximal value of these new complexities is attained in the case q=1.