Structural Statistical Quantifiers and Thermal Features of Quantum Systems

Abstract

This paper deals primarily with relatively novel thermal quantifiers called disequilibrium and statistical complexity, whose role is growing in different disciplines of physics and other sciences. These quantifiers are called L. Ruiz, Mancini, and Calvet (LMC) quantifiers, following the initials of the three authors who advanced them. We wish to establish information-theoretical bridges between LMC structural quantifiers and (1) Thermal Heisenberg uncertainties ΔxΔp (at temperature T); (2) A nuclear physics fermion model. Having achieved such purposes, we determine to what an extent our bridges can be extended to both the semi-classical and classical realms. In addition, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.

Quantum Purity as an Information Measure and Nernst Law

“…Now, introducing Equation (20) into Equation ( 15), we find the entropy S can be cast as a function of just D [17]. Thus, we reach the wished-for possibility of expressing the entropy solely in terms of the purity…”

“…Therefore, the purity is of course bounded, i.e., The above relation ( 18 ) shows that for small the hyperbolic tangent above approaches . From Equation ( 18 ), we can isolate the variable in the fashion Now, introducing Equation ( 20 ) into Equation ( 15 ), we find the entropy S can be cast as a function of just D [ 17 ]. Thus, we reach the wished-for possibility of expressing the entropy solely in terms of the purity We clearly see that maximum D yields zero entropy, and the third law of thermodynamics can be applied in terms of purity.…”