Reaction rates in quasiequilibrium states

Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on processes and quantities that strongly depend on the energy distribution, such as reaction rates. In this paper, we investigate reaction rates in the general context of quasiequilibrium systems, which exhibit only local equilibrium. The hierarchical structure of these systems allows their statistical properties to be represented as a superposition of statistics, i.e., superstatistics. Focusing on the three universality classes of superstatistics-χ^{2}, inverse-χ^{2}, and log-normal-we examine how these nonequilibrium distributions influence reaction rates. We analyze, both analytically and numerically, reaction rates for processes involving tunneling phenomena, such as fusion, and identify conditions under which quasiequilibrium distributions outperform Maxwellian distributions in enhancing fusion reactivities. To provide a more detailed quantitative analysis, we further employ semiempirical cross sections to evaluate the effect of these nonequilibrium distributions on ionization and recombination rates in a plasma.

Influence of thermal fluctuations on bosonic correlations and the ac Stark effect in two-level atoms: A superstatistical perspective

We study the influence of thermal fluctuations on the two-time correlation functions of bosonic baths within a superstatistics framework by assuming that fluctuations follow the gamma distribution. We further establish a connection between superstatistics and Tsallis nonadditive thermodynamics by introducing a temperature-renormalizing parameter. Our results show that, for an Ohmic model, the system's correlation functions exhibit diverse time-dependent behaviors, with the real and imaginary parts displaying enhancement or suppression depending on temperature and fluctuation strength. Additionally, we analyze the impact of these fluctuations on the quantum master equation of a damped two-level atom coupled to an out-of-equilibrium radiation bath. We demonstrate that while the equation's algebraic structure remains intact, the coupling constants are modified by the fluctuation parameters and cavity volume. Specifically, we observe that the ac Stark effect undergoes significant modifications, with fluctuations influencing the transition between repulsive and attractive energy levels.

Superstatistics Applied to Cucurbitaceae DNA Sequences

The short and long statistical correlations are essential in the genomic sequence. Such correlations are long-range for introns, whereas, for exons, these are short. In this study, we employed superstatistics to investigate correlations and fluctuations in the distribution of nucleotide sequence lengths of the Cucurbitaceae family. We established a time series for exon sizes to probe these correlations and fluctuations. We used data from the National Center for Biotechnology Information (NCBI) gene database to extract the temporal evolution of exon sizes, measured in terms of the number of base pairs (bp). To assess the model's viability, we utilized a timescale extraction method to determine the statistical properties of our time series, including the local distribution and fluctuations, which provide the exon size distributions based on the q-Gamma and inverse q-Gamma distributions. From the Bayesian statistics standpoint, both distributions are excellent for capturing the correlations and fluctuations from the data.

Superstatistics from a dynamical perspective: Entropy and relaxation

Distributions that deviate from equilibrium predictions are commonly observed across a broad spectrum of systems, ranging from laboratory experiments to astronomical phenomena. These distributions are generally regarded as a manifestation of a quasiequilibrium state and can very often be represented as a superposition of statistics, i.e., superstatistics. The underlying idea in this methodology is that the nonequilibrium system consists of a collection of smaller subsystems that remain infinitely close to equilibrium. This procedure has been effectively implemented in a kinetic setting, but thus far, only in the collisionless regime, limiting its scope of application. In this paper, we address the effect of collisions on the relaxation process and time evolution of superstatistical systems. After confronting the superstatistical distributions with experimental and simulation data, relevant to our analysis, we first study the effect of superstatistics on entropy. We explicitly show that, in the absence of long-range interactions, the extensivity of entropy is preserved, albeit influenced by the specific class of temperature fluctuations. Then, we examine how collisions drive the system towards a global equilibrium state, characterized by a maximum entropy, by employing the relaxation time approximation. This allows us to define a dynamical version of superstatistics, characterized by a singular time-varying parameter q(t), which undergoes a continuous evolution towards equilibrium. We show how this approach enables the determination of the evolution of the underlying temperature distribution under the influence of collisions, which act as stochastic forces, gradually narrowing the temperature distribution over time.

Kappa distribution from particle correlations in nonequilibrium, 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 modeling 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 nonadditivity 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 nonequilibrium 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 κ and the thermal velocity v_{th}.

Superstatistical and DNA sequence coding of the human genome

In this work, by considering superstatistics we investigate the short-range correlations (SRCs) and the fluctuations in the distribution of lengths of strings of nucleotides. To this end, a stochastic model provides the distributions of the size of the exons based on the q-Gamma and inverse q-Gamma distributions. Specifically, we define a time series for exon sizes to investigate the SRC and the fluctuations through the superstatistics distributions. To test the model's viability, we use the Project Ensembl database of genes to extract the time evolution of exon sizes, calculated in terms of the number of base pairs (bp) in these biological databases. Our findings show that, depending on the chromosome, both distributions are suitable for describing the length distribution of human DNA for lengths greater than 10 bp. In addition, we used Bayesian statistics to perform a selection model approach, which revealed weak evidence for the inverse q-Gamma distribution for a considerable number of chromosomes.

Generalized statistical mechanics of stellar systems

The observed distributions of stellar parameters, in particular, rotational and radial velocities, often depart from the Maxwellian (Gaussian) distribution. In the absence of a consistent statistical framework, these distributions are, in general, accounted for phenomenologically by employing power-law distributions, such as Tsallis or Kaniadakis distributions. Here we argue that the observed distributions correspond to locally Gaussian distributions, whose characteristic width is regarded as a statistical variable, in accordance with common knowledge that this parameter is mass dependent. The distributions arising within this picture correspond to superstatistics-a formalism emerging naturally in the context of self-gravitating media. We discuss in detail the distributions arising within this formalism and confront them with observational data of open clusters. We compute their moments and show that the Chandrasekhar-Münch relation remains invariant in this scenario. We also address the effect of these distributions on the thermalization of a massive body, e.g., a supermassive black hole, immersed in a stellar gas. We further discuss how the superstatistical picture clarifies certain ambiguities while offering a whole family of distributions (of which asymptotic power laws represent a special case), opening possibilities for fitting observational data.

Superstatistics and quantum entanglement in the isotropic spin-1/2 XX dimer from a nonadditive thermodynamics perspective

In this paper, the impact of temperature fluctuations in the entanglement of two qubits described by a spin-1/2 XX model is studied. To describe the out-of-equilibrium situation, superstatistics is used with fluctuations given by a χ^{2}-distribution function, and its free parameters are chosen in such a way that resembles the nonadditive Tsallis thermodynamics. In order to preserve the Legendre structure of the thermal functions, particular energy constraints are imposed on the density operator and the internal energy. Analytical results are obtained using an additional set of constraints after a parametrization of the physical temperature. We show that the well-known parametrization may lead to undesirable values of the physical temperature so that by analyzing the entropy as a function of energy, the correct values are found. The quantum entanglement is obtained from the concurrence and is compared with the case when the Tsallis restrictions are not imposed on the density operator.