Verlinde conjectured that gravitation is an emergent entropic force. This surprising conjecture was proved in [Physica A 505 (2018) 190] within a purely classical context. Here, we appeal to a quantum environment to deal with the conjecture in the case of bosons and consider also the classical limit of quantum mechanics (QM).
We study the classical statistical mechanics of a phase-space curve.This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom. Additionally, we obtain negative specific heats, a distinctive feature of self-gravitating systems and negative pressures, typical of dark energy.
In this work, a general definition of convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tem- * This work was partially supported by Consejo Nacional de Investigaciones Científicas and Comisión de Investigaciones Científicas de la Pcia. de Buenos Aires; Argentina.
Tsallis' q-Fourier transform is not generally one-to-one. It is shown here that, if we eliminate the requirement that q be fixed, and let it instead "float", a simple extension of the F q −definition, this procedure 1 restores the one-to-one character.
We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in the Renyi's variational problem (MaxEnt). This relation connects the two associated Lagrange multipliers (Canonical Ensemble) with the mean energy < U > and the Renyi parameter α. As a consequence of such relation, we obtain anomalous RenyiMaxEnt thermodynamic results.
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