Related papers: Canonical partition function for anomalous systems…
In classical thermodynamics the entropy is an extensive quantity, i.e.\ the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity…
The standard (non-relativistic) $\kappa$-distribution is widely used to fit data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure (temperature) as the second moment of the distribution function. By contrast to a…
The recently developed concept of "entropic defect" is important for understanding the foundations of thermodynamics in space plasma physics, and more generally, for systems with physical correlations among their particles. Using this…
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature…
A Kappa distribution function applicable to systems comprising mixed fermions and bosons has been developed through the thermodynamic Gibbs potential utilizing the quantum versions of the Olbert kappa distributions. The generalised…
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use…
It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
The generally accepted representation of $\kappa$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $\kappa$-independent. The present paper aims…
The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa}(f)=\frac{1}{2\kappa}\sum_i (f_i^{1-\kappa}-f_i^{1+\kappa})$ with $0<\kappa<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is…
This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that the polytropic…
A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only…
Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{\kappa\ell}$, associated with a Kappa-type power-law velocity distribution, $F_{\kappa\ell}(v)$, recently derived in the literature. By formulating…
Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…
We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(n,a), defined as the number of decompositions of a positive integer 'n'…
The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the…
Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of…
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…