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The Thermal Statistics of Quasi‐Probabilities’ Analogs in Phase Space

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  • F. Pennini
  • A. Plastino
  • M. C. Rocca

Abstract

We focus attention upon the thermal statistics of the classical analogs of quasi‐probabilities (QP) in phase space for the important case of quadratic Hamiltonians. We consider the three more important OPs: Wigner’s, P‐, and Husimi’s. We show that, for all of them, the ensuing semiclassical entropy is a function only of the fluctuation product ΔxΔp. We ascertain that the semiclassical analog of P‐distribution seems to become unphysical at very low temperatures. The behavior of several other information quantifiers reconfirms such an assertion in manifold ways. We also examine the behavior of the statistical complexity and of thermal quantities like the specific heat.

Suggested Citation

  • F. Pennini & A. Plastino & M. C. Rocca, 2015. "The Thermal Statistics of Quasi‐Probabilities’ Analogs in Phase Space," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:145684
    DOI: 10.1155/2015/145684
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    References listed on IDEAS

    as
    1. Mizrahi, S.S., 1988. "Quantum mechanics in the gaussian wave-packet phase space representation III: From phase space probability functions to wave-functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(3), pages 541-554.
    2. Pennini, F. & Plastino, A. & Ferri, G.L., 2007. "Semiclassical information from deformed and escort information measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 782-796.
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