arXiv subjects
Publications and source records attributed to A. Plastino.
We show that extremely simple systems of a not too large number of particles can be simultane- ously 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.
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.
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.
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.
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.
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.
That of disequilibrium (D) is a statistical notion introduced by López-Ruiz, Mancini, and Calbet (LMC) more than 20 years ago [Phys. Lett. A 209 (1995) 321]. D measures the amount of correlational structure of a system. We wish to use D to analyze one of the simplest types of quantum correlations, those present in simple quantum gaseous systems and due to symmetry considerations. To this end we extend the LMC formalism to the grand canonical environment and show that D displays distinctive behaviors for simple gases, that allow for interesting insights into their structural properties.
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.
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
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.
We analyze an exhaustive data-set of new-cars monthly sales. The set refers to 10 years of Spanish sales of more than 6500 different car model configurations and a total of 10M sold cars, from January 2007 to January 2017. We find that for those model configurations with a monthly market-share higher than 0.1% the sales become scalable obeying Gibrat's law of proportional growth under logistic dynamics. Remarkably, the distribution of total sales follows the predictions of the Maximum Entropy Principle for systems subject to proportional growth in dynamical equilibrium. We also encounter that the associated dynamics are non-Markovian, i.e., the system has a decaying memory or inertia of about 5 years. Thus, car sales are predictable within a certain time-period. We show that the main characteristics of the dynamics can be described via a construct based upon the Langevin equation. This construct encompasses the fundamental principles that any predictive model on car sales should obey.
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.
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.
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.
Gravitational Sound clips produced by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Massachusetts Institute of Technology (MIT) are considered within the particular context of data reduction. It is shown that these types of signals can be approximated at high quality using much less elementary components than those required within the standard orthogonal basis framework. Furthermore, a measure a local sparsity is shown to render meaningful information about the variation of a signal along time, by generating a set of local sparsity values which is much smaller than the dimension of the signal. This point is stressed further by recourse to a more complex signal, generated by Milde Science Communication to divulge Gravitational Sound in the form a ring tone.
\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 $q\rightarrow 1$.}
A robust prediction model invoking the Takens embedding theorem, whose \textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz, central to the \textit{working hypothesis} satisfy a time independent Schrödinger-like equation in a vector setting. The inference of i) the probability density function of the coefficients of the \textit{working hypothesis} and ii) the establishing of constraint driven pseudo-inverse condition for the modeling phase of the prediction scheme, is made, for the case of normal distributions, with the aid of the quantum mechanical virial theorem. The well-known reciprocity relations and the associated Legendre transform structure for the Fisher information measure (FIM, hereafter)-based model in a vector setting (with least square constraints) are self-consistently derived. These relations are demonstrated to yield an intriguing form of the FIM for the modeling phase, which defines the \textit{working hypothesis}, solely in terms of the observed data. Cases for prediction employing time series' obtained from the: $(i)$ the Mackey-Glass delay-differential equation, $(ii)$ one ECG sample from the MIT-Beth Israel Deaconess Hospital (MIT-BIH) cardiac arrhythmia database, and $(iii)$ one ECG from the Creighton University ventricular tachyarrhythmia database. The ECG samples were obtained from the Physionet online repository. These examples demonstrate the efficiency of the prediction model. Numerical examples for exemplary cases are provided.
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.