Thermodynamics’ first law (TFL), although undoubtedly true because of its many verified consequences, rests on a rather weak experimental foundation in the sense that, as pointed out by Pippard, its path-independent aspect cannot be said to have been directly verified. From the theoretical...

There exist two different versions of the Kullback–Leibler divergence (K–Ld) in Tsallis statistics, namely the usual generalized K–Ld and the generalized Bregman K–Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized...

We investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using Tsallis q-entropy as a quantifier of the ensuing dynamics, we find that it not only appropriately describes the...

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer–Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures....

We report on the fact that microscopically enforcing fulfillment of thermodynamics’ third law on a system of fermions automatically yields the values of the external parameter (here coupling strengths in the pertinent Hamiltonian) at which quantum phase transitions take place. Our...

q-Gaussian behavior is often encountered in quite distinct settings. A possible explanation is here given with reference to experimental scenarios in which data are gathered using a set-up that performs a normalization preprocessing. We show that the ensuing normalized input, as recorded by the...

We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of the Fisher information measure. In such a way a clear analogy between these systems’ thermal properties and those of gases and fluids is seen to emerge in a natural fashion. We...

Non-extensive thermostatistics is a new paradigm statistical mechanics (SM) that has reached the rather mature age of 15 in 2003. It has considerably extended both SM formalism and its range of applicability. It constitutes one of physics’ new frontiers, with advances being made almost on a...

The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant subspaces are well separated the problem is readily solvable...

We show here how to use pieces of thermodynamics’ first law to generate probability distributions for generalized ensembles when only level-population changes are involved. Such microstate occupation modifications, if properly constrained via first law ingredients, can be associated not...