arXiv subjects

Sergio Davis

Publications and source records attributed to Sergio Davis.

At least 19 recordsLinked to original sources

arXiv2026

Kappa distributions as asymptotic marginals of exponential family ensembles

Recently (Physica A 660 130370, 2025), emergence of superstatistical behavior in driven classical systems has been shown for systems with constant microcanonical heat capacity. As an application of this result, in this work we show that a system of $N$ particles with inverse gamma distribution of total kinetic energies must have kappa-distributed single-particle velocities in the limit $N \rightarrow \infty$. Our results provide insight into the nature of kappa distributions outside the theory of nonextensive statistical mechanics, while also bringing forward a practical method for the generation of kappa velocities via Monte Carlo Metropolis simulation in the inverse gamma ensemble.

cond-mat.stat-mech↗

arXiv2026

Parameter estimation for kappa distributions using the EM algorithm in the superstatistical framework

Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not belong to the exponential family, so it admits no sufficient statistics and direct maximum likelihood requires numerical optimization without analytically closed-form update equations. Working within the Beck-Cohen superstatistics framework, where a gamma-distributed inverse temperature $\beta$ generates the kappa distribution upon marginalization, we treat $\beta$ as a latent variable. This hierarchical description restores the exponential family structure that the marginal kappa distribution lacks, and yields an analytically tractable implementation of the expectation-maximization (EM) algorithm whose E-step and M-step admit closed-form expressions in terms of sufficient statistics. Applied to synthetic data drawn from the model, the algorithm converges monotonically to a stationary point of the marginal kappa log-likelihood and recovers the generating parameters consistently across the explored range of $\kappa$. EM thus offers a tractable and transparent route to inference in superstatistical systems with local temperature fluctuations.

stat.ME↗

arXiv2026

Fundamental temperature in the superstatistical description of non-equilibrium steady states

Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention. Superstatistics postulates a superposition of canonical systems with inverse temperatures $\beta$ described by a probability distribution depending on the external conditions. Unfortunately, the uncertainty about $\beta$ cannot be attributed to fluctuations of a phase space function, and this suggests that the distribution of $\beta$ is purely of statistical nature and must be inferred rather than measured. This lack of direct observability of the superstatistical temperature then becomes a conceptual issue in need of resolution. In this work we address this issue, showing that a mapping exists between functions of the superstatistical temperature and functions of the recently proposed fundamental temperature, a model-dependent function of the energy, in such a way that their expectation values coincide. We illustrate the use of this mapping by computing the conditional distribution of inverse temperature given energy for the $q$-canonical ensemble, as well as the full inverse temperature distribution, without the use of Laplace inversion.

cond-mat.stat-mech↗

arXiv2026

Kinetic energy fluctuations and specific heat in generalized ensembles

We derive an exact generalization of the well-known Lebowitz--Percus--Verlet (LPV) formula that relates the kinetic energy fluctuations of an isolated system to its specific heat. Our general formula, obtained by the application of expectation identities, is valid for arbitrary steady--state ensembles and system sizes, expressing the relative variance of the kinetic energy in terms of the variance of total energy and the microcanonical specific heat. The usual microcanonical LPV formula can be readily recovered as a particular case where energy fluctuations vanish. We test the validity of the generalized formula by performing Monte Carlo simulations of a superstatistical system of harmonic oscillators, as well as by exact calculation of energy variances in a uniform--energy ensemble, discussing its relevance to systems exhibiting negative heat capacity and ensemble inequivalence, as encountered in finite nuclei and self--gravitating models. Our results may provide useful in the study of non-equilibrium phase transitions in finite systems.

cond-mat.stat-mech↗

arXiv2025

Unifying Kappa Distribution Models for Non-Equilibrium Space Plasmas: A Superstatistical Approach Based on Moments

From the perspective of non-equilibrium statistical mechanics, modeling the velocity distribution of particles in non-equilibrium, steady-state plasmas presents a significant challenge. Under this context, a family of kappa distributions has been widely used to capture the high-energy tails in space plasmas. These distributions deviate from the canonical Maxwell-Boltzmann statistics and vary significantly in their interpretation of the temperature of an out-of-equilibrium system. In this letter, we establish the validity of any kappa distribution from the standpoint of superstatistics. This study unifies these models by introducing a new kappa distribution based on superstatistical parameters, providing a more general and fundamental framework to connect these distributions and the superstatistical temperature of a system. We demonstrate that the general distribution depends on the thermal characteristics of the modeled temperature distribution population. Furthermore, we present a moment-based velocity distribution that bypasses the traditional temperature debate, relying on the velocity moments. Our findings enhance the understanding of kappa distributions and offer a robust model for non-equilibrium space plasmas.

physics.plasm-ph↗

arXiv2025

Configurational density of states of finite classical systems

The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for non-trivial systems, and numerical algorithms such as Wang-Landau simulation are often used. In this work we use a microcanonical framework to provide an explicit inversion formula for the calculation of the CDOS from the total density of states (DOS) without resorting to the inversion of the Laplace transform. From this formula, several results can be obtained for the thermodynamics of finite classical systems composed of a few degrees of freedom, while also recovering the well-known asymptotic results for the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2025

Configurational density of states of power-law potentials and the virial theorem in steady states

In this brief note, the configurational density of states of a system of particles interacting via power-law pair potentials is computed exactly. The result is consistent with a constant microcanonical heat capacity. The well-known form of the virial theorem for this class of systems is recovered using only the obtained configurational density of states, and shown to be valid beyond the canonical and microcanonical ensembles, in general steady states.

cond-mat.stat-mech↗

arXiv2025

Closure of superstatistics

Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such as superstatistics, where steady states are treated as superpositions of canonical ensembles under a temperature distribution. In this work we solve the problem of inferring the possible steady states of a composite system $AB$ where subsystem $A$ is described by superstatistics and $E_{AB} = E_A + E_B$. Our result establishes a closure property of superstatistics, namely that $A$ is described by superstatistics if and only if $AB$ and $B$ are also superstatistical with the same temperature distribution. Some consequences of this result are discussed, such as the impossibility of local thermal equilibrium (LTE) for additive subsystems in non-canonical steady states.

cond-mat.stat-mech↗

arXiv2025

Kappa distributions in the framework of superstatistics

The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified through the use of Tsallis' non-extensive statistics, nowadays there are alternative frameworks that provide insight into these distributions, such as superstatistics. In this work we review the derivation of the multi-particle and single-particle kappa distributions for collisionless plasmas within the framework of superstatistics, as an alternative to the use of non-extensive statistics. We also show the utility of the superstatistical framework in the computation of expectation values under kappa distributions. Some consequences of the superstatistical formalism regarding correlations, temperature and entropy of kappa-distributed plasmas are also discussed.

cond-mat.stat-mech↗

arXiv2024

Microcanonical Monte Carlo simulation of opinion dynamics under the influence of mass media

The formation of large social groups having uniform opinions influenced by mass media is currently an important topic in the social sciences. In this work, we explore and extend an off-lattice, two-dimensional Potts model (Eur. Phys. J. B 87, 78 [2014]) that describes the formation and dynamics of opinions in social groups according to individual consequence and agreement between neighbors. This model was originally obtained by the application of the maximum entropy principle, a general method in statistical inference, and using the same methodology we have now included the influence of mass media as a constant external field. By means of microcanonical Monte Carlo Metropolis simulations on a setup with two regions with opposing external influences, we have shown the presence of metastable states associated to the formation of clusters aligned with the locally imposed opinion. Our results suggest that, for some values of the total energy of the system, only a single cluster with a uniform opinion survives, thus the presence of two large, opposing groups is not a thermodynamically stable configuration.

physics.soc-ph↗

arXiv2024

Temperature and equipartition in discrete systems

The generalized equipartition theorem known as the conjugate variables theorem (Phys. Rev. E 86, 051136 [2012]), originally obtained in the context of statistical inference of continuous random variables, is extended in this work to the case of discrete variables. Using this new set of theorems we derive novel thermodynamic identities for the canonical ensemble connecting temperature with measurable observables.

cond-mat.stat-mech↗

arXiv2024

Superstatistics as the thermodynamic limit of driven classical systems

Superstatistics is an elegant framework for the description of steady-state thermodynamics, mostly used for systems with long-range interactions such as plasmas. In this work, we show that the potential energy distribution of a classical system under externally imposed energy fluctuations can also be described by superstatistics in the thermodynamic limit. As an example, we apply this formalism to the thermodynamics of a finite Lennard-Jones crystal with constant microcanonical heat capacity driven by sinusoidal energy oscillations. Our results show that molecular dynamics simulations of the Lennard-Jones crystal are in agreement with the provided theoretical predictions.

cond-mat.stat-mech↗

arXiv2024

A quantum expectation identity: Applications to statistical mechanics

In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between different quantum observables depending on a continuous parameter. Such a parameter can be contained in the observables itself (e.g. perturbative parameter) or may appear as a Lagrange multiplier (inverse temperature, chemical potential, etc.) in the density matrix, excluding parameters that modify the underlying Hilbert space. In this way, using both canonical and grand canonical density matrices along with certain quantum observables (Hamiltonian, number operator, the density matrix itself, etc.) we found new identities in the field, showing not only its derivation but also their meaning. Additionally, we found that some theorems of traditional quantum statistics and quantum chemistry, such as the thermodynamical fluctuation-dissipation theorem, the Ehrenfest, and the Hellmann-Feynman theorems, among others, are particular instances of our aforementioned quantum expectation identity. At last, using a generalized density matrix arising from the Maximum-Entropy principle, we derive generalized quantum expectation identities: these generalized identities allow us to group all the previous cases in a unitary scheme.

quant-ph↗

arXiv2024

A superstatistical measure of distance from canonical equilibrium

Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical theories such as non-extensive statistics and superstatistics. Superstatistics assumes that the inverse temperature $\beta = 1/(k_B T)$ follows some pre-established statistical distribution, however, it has been previously proved (Physica A 505, 864-870 [2018]) that $\beta$ cannot be associated to an observable function $B(\boldsymbol{\Gamma})$ of the microstates $\boldsymbol{\Gamma}$. In this work, we provide an information-theoretical interpretation of this theorem by introducing a new quantity $\mathcal{D}$, the mutual information between $\beta$ and $\boldsymbol{\Gamma}$. Our results show that $\mathcal{D}$ is also a measure of departure from canonical equilibrium, and reveal a minimum, non-zero uncertainty about $\beta$ given $\boldsymbol{\Gamma}$ for every non-canonical superstatistical ensemble. This supports the use of the mutual information as a descriptor of complexity and correlation in complex systems, also providing in some cases a sound basis for the use of Tsallis' entropic index $q$ as a measure of distance from equilibrium, being in those cases a proxy for $\mathcal{D}$.

cond-mat.stat-mech↗

arXiv2023

Fundamental temperature exclusively determines the validity of superstatistics

The theory of superstatistics is a generalization of Boltzmann-Gibbs statistical mechanics which admits temperature fluctuations, and generates non-canonical ensembles from the distribution function of these fluctuations. Recently, some results have been presented showing that superstatistics is not universally applicable, but several conditions on the so-called fundamental inverse temperature function $\beta_F$ must be met by any superstatistical model. In this work we provide a set of neccessary and sufficient conditions for a non-equilibrium steady state model to be expressible by superstatistics, showing that $\beta_F$ by itself determines the existence of a superstatistical distribution of temperature.

cond-mat.stat-mech↗

arXiv2023

Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas

Kappa-distributed velocities in plasmas are common in a wide variety of settings, from low-density to high-density plasmas. To date, they have been found mainly in space plasmas, but are recently being considered also in the modelling of laboratory plasmas. Despite being routinely employed, the origin of the kappa distribution remains, to this day, unclear. For instance, deviations from the Maxwell-Boltzmann distribution are sometimes regarded as a signature of the non-additivity of the thermodynamic entropy, although there are alternative frameworks such as superstatistics where such an assumption is not needed. In this work we recover the kappa distribution for particle velocities from the formalism of non-equilibrium steady-states, assuming only a single requirement on the dependence between the kinetic energy of a test particle and that of its immediate environment. Our results go beyond the standard derivation based on superstatistics, as we do not require any assumption about the existence of temperature or its statistical distribution, instead obtaining them from the requirement on kinetic energies. All of this suggests that this family of distributions may be more common than usually assumed, widening its domain of application in particular to the description of plasmas from fusion experiments. Furthermore, we show that a description of kappa-distributed plasma is simpler in terms of features of the superstatistical inverse temperature distribution rather than the traditional parameters $\kappa$ and the thermal velocity $v_{\text{th}}$.

cond-mat.stat-mech↗

arXiv2023

Prediction and Retrodiction in Statistical Mechanics from the Principle of Maximum Caliber

A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical mechanical models from a variational principle, provided that the adequate time-dependent constraints and the state of the system at some specific times are given. The approach is exemplified by obtaining the description of a time-dependent Brownian particle from kinetic restrictions. We relate the predictive nature of a model to the structure of the prior distribution that represents the state of knowledge about the system before the dynamical constraints are considered. Non-predictive models are shown to be possible in the presented framework and as an example, retrodictive dynamics are obtained from the same kinetic constraints.

cond-mat.stat-mech↗

arXiv2022

Configurational density of states and melting of simple solids

We analyze the behavior of the microcanonical and canonical caloric curves for a piecewise model of the configurational density of states of simple solids, in the context of melting from the superheated state, as realized numerically in the Z-method via atomistic molecular dynamics. A first-order phase transition with metastable regions is reproduced by the model, being therefore useful to describe aspects of the melting transition. Within this model, transcendental equations connecting the superheating limit, the melting point, and the specific heat of each phase are presented and numerically solved. Our results suggest that the essential elements of the microcanonical Z curves can be extracted from simple modeling of the configurational density of states.

cond-mat.stat-mech↗