arXiv subjects

M. C. Rocca

Publications and source records attributed to M. C. Rocca.

At least 37 records · Page 2Linked to original sources

arXiv2018

On the entropic derivation of the $r^{-2}$ Newtonian gravity force

Following Verlinde's conjecture, we show that Tsallis' classical free particle distribution at temperature $T$ can generate Newton's gravitational force's $r^{-2}$ {\it distance's dependence}. If we want to repeat the concomitant argument by appealing to either Boltzmann-Gibbs' or Renyi's distributions, the attempt fails and one needs to modify the conjecture. Keywords: Tsallis', Boltzmann-Gibbs', and Renyi's distributions, classical partition function, entropic force.

gr-qc↗

arXiv2018

Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation

It is believed that the canonical gravitational partition function $Z$ associated to the classical Boltzmann-Gibbs (BG) distribution $\frac {e^{-βH}} {\cal Z}$ cannot be constructed because the integral needed for building up $Z$ includes an exponential and thus diverges at the origin. We show here that, by recourse to 1) the analytical extension treatment obtained for the first time ever, by Gradshteyn and Rizhik, via an appropriate formula for such case and 2) the dimensional regularization approach of Bollini and Giambiagi's (DR), one can indeed obtain finite gravitational results employing the BG distribution. The BG treatment is considerably more involved than its Tsallis counterpart. The latter needs only dimensional regularization, the former requires, in addition, analytical extension.

physics.gen-ph↗

arXiv2018

Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation

Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function ${\cal Z}$ and the mean energy $<{\cal U}>$. 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.

cond-mat.stat-mech↗

arXiv2017

Reply to "Comment on "Troublesome aspects of the Renyi-MaxEnt treatment""

This Reply is intended as a refutation of the preceding Comment [Oikonomou and Bagci, Phys. Rev. E 96, 056101 (2017)] on our paper [Plastino et al., Phys. Rev. E 94, 012145 (2016).]. We show that the Tsallis probability distribution of our paper does not coincide with the Tsallis distribution studied by Oikonomou and Bagci. Consequently, their findings do not apply to our paper.

cond-mat.stat-mech↗

arXiv2017

q-Path entropy phenomenology for phase-space curves

We describe the phenomenology of the classical q-path entropy of a phase-space curve. This allows one to disclose an entropic force-like mechanism that is able to mimic some phenomenological aspects of the strong force, such as confinement, hard core, and asymptotic freedom.

cond-mat.stat-mech↗

arXiv2017

Dimensional Regularization of Renyi's Statistical Mechanics

We show that typical Renyi's statistical mechanics' quantifiers exhibit poles. We are referring to the partition function ${\cal Z}$ and the mean energy $<{\cal U}>$. 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.

cond-mat.stat-mech↗

arXiv2017

The Tachyon Propagator

Following the canonical quantization procedure for a tachyon field, the usual Hamiltonian and the creation and annihilation operators are obtained. The observation that the mass hyperboloid $p^2-m^2=0$ is one-sheeted, as opposed to the case of bradyons where $p^2+m^2=0$ is two-sheeted, leads to the construction of a base which is unbounded for negative as well as for positive energies. There is a zero-energy eigenfunction from which all other states can be constructed by repeated application of decreasing or increasing operators, within this Fock space the vacuum expectation value of the chronological product of field operators is shown to coincide with Cauchy's principal-value Green's function.

hep-th↗

arXiv2017

The Tachyon Field below the mass barrier

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have them a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof [4] that the total propagator is the Wheeler Green function [4,7].

hep-th↗

arXiv2017

Quantum q-Field Theory: q-Schrödinger and q-Klein-Gordon Fields

We show how to deal with the generalized q-Schrödinger and q-Klein-Gordon fields in a variety of scenarios. These q-fields are meaningful at very high energies (TeVs) for for $q=1.15$, high ones (GeVs) for $q=1.001$, and low energies (MeVs)for $q=1.000001$ [Nucl. Phys. A {\bf 948} (2016) 19, Nucl. Phys. A {\bf 955} (2016) 16]. We develop here the quantum field theory (QFT) for the q-Schrödinger and q-Klein-Gordon fields, showing that both reduce to the customary Schrödinger and Klein-Gordon QFTs for q close to unity. Further, we analyze the q-Klein-Gordon field for $2q-1=n$ (n integer $\ge 2$) and analytically compute the self-energy and the propagator up to second order.

hep-th↗

arXiv2017

Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial

It ts known that Tsallis' q-non-additivity entails hidden correlations. It has also been shown that even for a monoatomic gas, both the q-partition function $Z$ and the mean energy $ $ diverge and, in particular, exhibit poles for certain values of the Tsallis non additivity parameter $q$. This happens because $Z$ and $ $ both depend on a $Γ$-function. This $Γ$, in turn, depends upon the spatial dimension $ν$. We encounter three different regimes according to the argument $A$ of the $Γ$-function. (1) $A>0$, (2) $A<0$ and $Γ>0$ outside the poles. (3) $A$ displays poles and the physics is obtained via dimensional regularization. In cases (2) and (3) one discovers gravitational effects and quartets of particles. Moreover, bound states and gravitational effects emerge as a consequence of the hidden q-correlations.

cond-mat.stat-mech↗

arXiv2017

Analysis of Tsallis' classical partition function's poles

When one integrates the q-exponential function of Tsallis' so as to get the partition function $Z$, a gamma function inevitably emerges. Consequently, poles arise. We investigate here here the thermodynamic significance of these poles in the case of $n$ classical harmonic oscillators (HO). Given that this is an exceedingly well known system, any new feature that may arise can safely be attributed to the poles' effect. We appeal to the mathematical tools used in [EPJB 89, 150 (2016) and arXiv:1702.03535 (2017)], and obtain both bound and unbound states. In the first case, we are then faced with a classical Einstein crystal. We also detect what might be interpreted as pseudo gravitational effects.

cond-mat.stat-mech↗

arXiv2017

On the putative essential discreteness of q-generalized entropies

It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of non-extensive statistical mechanics". The arguments are clever and appealing. We show here that, however, some mathematical subtleties render them unconvincing

cond-mat.stat-mech↗

arXiv2017

In defense of Tsallis' original probability distribution

Tsallis' pioneer q-probability distribution $P_i=\frac {[1+β(1-q)U_i]^{\frac {1} {q-1}}} {Z}$, $Z=\sum\limits_{i=1}^n [1+β(1-q)U_i]^{\frac {1} {q-1}}$ [J. of Stat. Phys., {\bf 52} (1988) 479] has been recently attacked in arXiv:1705.01752, in a Reply to our arXiv:1704.07493 publication. We show here that such an attack is groundless.

cond-mat.stat-mech↗

arXiv2017

Strong correlations between the exponent $α$ and the particle number for a Renyi-monoatomic gas in Gibbs' statistical mechanics

Appealing to the 1902 Gibbs' formalism for classical statistical mechanics (SM), the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics, we will here show that already at the classical level there is a strong correlation between the Renyi's exponent $α$ and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.

cond-mat.stat-mech↗

arXiv2017

Rescuing the MaxEnt treatment for $q$-generalized entropies

It has been recently argued, via very clever arguments, 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.

cond-mat.stat-mech↗

arXiv2017

New mathematics for the non additive Tsallis' scenario

In this manuscript we investigate quantum uncertainties in a Tsallis' non additive scenario. To such an end we appeal to q-exponentials, that are the cornerstone of Tsallis' theory. In this respect, it is found that some new mathematics is needed and we are led to construct a set of novel special states that are the q-exponential equivalents of the ordinary coherent states of the harmonic oscillator. We then characterize these new Tsallis' special states by obtaining the associated i) probability distributions for a state of momentum $k$, ii) mean values for some functions of space an momenta, and iii) concomitant quantum uncertainties. The latter are then compared to the usual ones.

quant-ph↗

arXiv2017

Classical and \textcolor{blue}{Quantum} Field-Theoretical approach to the non-linear q-Klein-Gordon Equation

\color{blue}{In the wake of efforts made in [EPL {\bf 97}, 41001 (2012)] and [J. Math. Phys. {\bf 54}, 103302 (2913)], we extend them here by developing the conventional Lagrangian treatment of a classical field theory (FT) to the q-Klein-Gordon equation advanced in [Phys. Rev. Lett. {\bf 106}, 140601 (2011)] and [J. Math. Phys. {\bf 54}, 103302 (2913)], and the quantum theory corresponding to $q=\frac {3} {2}$. This makes it possible to generate a putative conjecture regarding black matter. Our theory reduces to the usual FT for $q\rightarrow 1$.}

hep-th↗

arXiv2016

A first order Tsallis theory

We investigate first-order approximations to both i) Tsallis' entropy $S_q$ and ii) the $S_q$-MaxEnt solution (called q-exponential functions $e_q$). It is shown that the functions arising from the procedure ii) are the MaxEnt solutions to the entropy emerging from i). The present treatment is free of the poles that, for classic quadratic Hamiltonians, appear in Tsallis' approach, as demonstrated in [Europhysics Letters {\bf 104}, (2013), 60003]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.

cond-mat.stat-mech↗