Heisenberg-Fisher thermal uncertainty measure

• Autores: Pennini, Flavia; Plastino, Ángel Luis
• Año de publicación: 2004
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Física; Joint entropy; Entropy in thermodynamics and information theory; Wehrl entropy; H-theorem; Canonical ensemble; Mathematics; Mathematical physics; Joint quantum entropy; Maximum entropy thermodynamics; Partition function (statistical mechanics); Quantum mechanics
• Institución: Universidad Nacional de La Plata

We establish a connection among (i) the so-called Wehrl entropy, (ii) Fisher's information measure I(beta), and (iii) the canonical ensemble entropy for the one-dimensional quantum harmonic oscillator (HO). We show that the contribution of the excited HO spectrum to the mean thermal energy is given by Iβ, while the pertinent canonical partition function is essentially given by another Fisher measure: the so-called shift invariant one. Our findings should be of interest in view of the fact that it has been shown that the Legendre transform structure of thermodynamics can be replicated without any change if one replaces the Boltzmann-Gibbs-Shannon entropy by Fisher's information measure [Phys. Rev. E 60, 48 (1999)]]. Fisher-related uncertainty relations are also advanced, together with a Fisher version of thermodynamics' third law.
Instituto de Física La Plata