Related papers: The two parameters (k, r) in the generalized stati…
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
We perform a Taylor series expansion of Tsallis distribution by assuming the Tsallis parameter $q$ close to 1. The $q$ value shows the deviation of a system from a thermalised Boltzmann distribution. By taking up to first order in $(q-1)$,…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
We propose a generalization of classical statistical mechanics which describes the behavior of dissipative systems placed in contact with a heat bath. In contrast to conventional statistical mechanics, which assigns probabilities to the…
Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…
Superstatistics generalizes Boltzmann statistics by assuming spatio-temporal fluctuations of the intensive variables. It has many applications in the analysis of experimental and simulated data. The fluctuation of the intensity variable is…
This paper aims to justify the use of statistical mechanics tools in situations where the system is out of equilibrium and jammed. Specifically, we derive a Boltzmann equation for a jammed granular system and show that the Boltzmann's…
The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the…
We analyze the connection between $p_T$ and multiplicity distributions in a statistical framework. We connect the Tsallis parameters, $T$ and $q$, to physical properties like average energy per particle and the second scaled factorial…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
Preferences of individuals are distributions of elements generated by generalized functions. Models of economic decision-making derived from such distributions are consistent with results of physiological experiments, and explain any…
We examine the properties of distributions with the density of the form: $% \frac{2A_{n}c^{n-2}\sqrt{c^{2}-x^{2}}}{\pi \prod_{j=1}^{n}(c(1+a_{j}^{2})-2a_{j}x)},$ where $c,a_{1},\ldots ,a_{n}$ are some parameters and $A_{n}$ a suitable…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
A basic statistical mechanics analysis of many-body systems with non-reciprocal pair interactions is presented. Different non-reciprocity classes in two- and three-dimensional binary systems (relevant to real experimental situations) are…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…