Superstatistical two-temperature Ising model

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.

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.

Fluctuations of water quality time series in rivers follow superstatistics

Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate water quality time series (such as dissolved oxygen concentrations and electrical conductivity) as measured in rivers and provide evidence that they exhibit superstatistical behavior. Our main example is time series as recorded in the River Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by log-normal superstatistics for dissolved oxygen. Contrarily, we find a double peaked non-standard superstatistics for the electrical conductivity data, which we model using two combinedχ 2 -distributions.