Heisenberg-Fisher thermal uncertainty measure

Abstract

With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, 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 $I$, while the pertinent canonical partition function is given by another Fisher measure: the so-called shift invariant one, minus the HO's ground state energy. 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 [{\it Physical Review E} {\bf 60}, 48 (1999)]. New Fisher-related uncertainty relations are also advanced.

arXiv commentPhysical Review E (2004), in press

References in corpus (4)

• An Information-Theoretic Measure of Uncertainty due to Quantum and Thermal Fluctuations
• Thermodynamics of the harmonic oscillator using coherent states
• Power-Law distributions and Fisher's information measure
• How fundamental is the character of thermal uncertainty relations?

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• Dynamics of the Fisher Information Metric
• Delocalization and the semiclassical description of molecular rotation
• Quantum statistical information contained in a semi-classical Fisher--Husimi measure
• Classical thermodynamics from quasi-probabilities