A. Plastino

Dimensionally regularized Tsallis’ statistical mechanics and two-body Newton’s gravitation

Abstract Typical Tsallis’ statistical mechanics’ quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function Z and the mean energy 〈 U 〉 . The poles appear for distinctive values of Tsallis’ characteristic real parameter q , at a numerable set of rational numbers of the q -line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.

LIBOR Troubles: Anomalous Movements Detection Based on Maximum Entropy

According to the definition of the London Interbank Offered Rate (LIBOR), contributing banks should give fair estimates of their own borrowing costs in the interbank market. Between 2007 and 2009, several banks made inappropriate submissions of LIBOR, sometimes motivated by profit-seeking from their trading positions. In 2012, several newspapers’ articles began to cast doubt on LIBOR integrity, leading surveillance authorities to conduct investigations on banks’ behavior. Such procedures resulted in severe fines imposed to involved banks, who recognized their financial inappropriate conduct. In this paper, we uncover such unfair behavior by using a forecasting method based on the Maximum Entropy principle. Our results are robust against changes in parameter settings and could be of great help for market surveillance.

Dimensional regularization of Renyi’s statistical mechanics

Abstract We show that typical Renyi’s statistical mechanics’ quantifiers exhibit poles. We are referring to the partition function Z and the mean energy 〈 U 〉 . Renyi’s entropy is characterized by a real parameter α . The poles emerge in a numerable set of rational numbers belonging to the α -line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones. In particular, negative specific heats.

Rescuing the MaxEnt treatment for q-generalized entropies

Abstract It has been recently argued that the MaxEnt variational problem would not adequately work for Renyi’s and Tsallis’ entropies. We constructively show here that this is not so if one formulates the associated variational problem in a more orthodox functional fashion.

Statistical complexity without explicit reference to underlying probabilities

Abstract We show that extremely simple systems of a not too large number of particles can be simultaneously thermally stable and complex. To such an end, we extend the statistical complexity’s notion to simple configurations of non-interacting particles, without appeal to probabilities, and discuss configurational properties.

Quantum treatment of Verlinde’s entropic force conjecture

Abstract Verlinde conjectured that gravitation is an emergent entropic force. This surprising conjecture was proved in Plastino and Rocca (2018) 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).

Newton’s gravitation-force’s classical average proof of a Verlinde’s conjecture

Abstract A surprising, gravity related Verlinde-conjecture, that generated immense interest, asserts that gravity is an emergent entropic force. We provided a classical proof of the assertion in [ doi.org/j.physa.2018.03.019 ]. Here, we classically prove a related, second Verlinde-conjecture. This states that, at very large distances ( r 0 ), gravity departs from its classical nature and begins to decay linearly with r 0 .