2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20509It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. In this paper, we revisit this idea in connection with a detailed microscopic calculation of the energy and temperature fluctuations present in a finite vessel of perfect gas thermally coupled to a heat bath. We find that the probability density related to the inverse temperature of the gas has a form similar to a $χ^2$ density, and that the `mixed' Gibbs distribution inferred from this density is non-Gibbsian. These findings are compared with those obtained by a number of researchers who worked on mixtures of Gibbsian distributions in the context of velocity difference measurements in turbulent fluids as well as secondaries distributions in nuclear scattering experiments.14 pages, 2 figures; contribution to the International Workshop on Interdisciplinary Applications of Ideas from Nonextensive Statistical Mechanics and Thermodynamics, April 8-12, 2002, Santa Fe Institute, Santa Fe, New Mexico, USAStatistical Mechanicstext