2003/12/31 by F. Pennini, A. Plastino · 40 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Canonical ensemble #Cold Atom Physics and Bose-Einstein Condensates #Entropy (arrow of time) #Entropy in thermodynamics and information theory #Fisher information #Joint quantum entropy #Mathematical physics #Mathematics #Maximum entropy thermodynamics #Measure (data warehouse) #Physics #Principle of maximum entropy #Quantum mechanics #Second law of thermodynamics #Statistical Mechanics and Entropy #Statistical physics #Statistics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.057101
published in Physical Review E 69(5), 057101 (American Physical Society) · Physical Review E (2004), in press
arxiv created 2004/04/28 · openalex publication_date 2004/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 I(beta), 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.