M. H. Benetti | Searcharxiv

arXiv2025

Kappa Entropy and its Thermodynamic Connection

Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{κ\ell}$, associated with a Kappa-type power-law velocity distribution, $F_{κ\ell}(v)$, recently derived in the literature. By formulating an extended Neo-Boltzmannian microstate counting procedure and employing standard averaging techniques, we demonstrate that the fundamental laws of thermodynamics are preserved within this generalized power-law framework only whether $\ell=-5/2$, regardless of the values assumed by the $κ$-parameter.

cond-mat.stat-mech↗

arXiv2025

Unified Description of Kappa-type velocity distributions

An extension of Maxwell's original prescription for an ideal gas is adopted to derive a broad class of Kappa-type velocity distributions, encompassing both fat and short-tailed forms. Within this general framework, a physically consistent fat-tailed Kappa distribution is identified that accurately fits recent suprathermal data. In particular, a kinetic physical temperature $T$ emerges naturally from the model, eliminating the need to invoke an effective temperature $T_{κ\ell}$, as is commonly done in the literature. Finally, it is argued that only a particular value of $\ell$ ensures a satisfactory fit to the data when the physical kinetic temperature is employed.

physics.plasm-ph↗

arXiv2025

Non-Gaussian velocity distributions Maxwell would understand

In 1988, Constantino Tsallis proposed an extension of the Boltzmann statistical mechanics by postulating a new entropy formula, $S_q = k_B\ln_q W$, where $W$ is the number of microstates accessible to the system, and $\ln_q$ defines a deformation of the logarithmic function. This ``top-down" , approach recovers the celebrated Boltzmann entropy in the limit $q \rightarrow 1$ since $S_1 = k_B\ln W$. However, for $q\neq 1$ the entropy is non-additive and has been successfully applied for a variety of phenomena ranging from plasma physics to cosmology. For a system of particles, Tsallis' formula predicts a large class of power-law velocity distributions reducing to the Maxwellian result only for a particular case. Here a more pedagogical ``bottom-up" path is adopted. We show that a large set of power-law distributions for an ideal gas in equilibrium at temperature T is derived by slightly modifying the seminal Maxwell approach put forward in 1860. The emergence of power-laws velocity distribution is not necessarily related with the presence of long-range interactions. It also shed some light on the long-standing problem concerning the validity of the zeroth law of thermodynamics in this context. Potentially, since the new method highlights the value of hypotheses in the construction of a basic knowledge, it may have an interesting pedagogical and methodological value for undergraduate and graduate students of physics and related areas.

cond-mat.stat-mech↗