arXiv subjects

M. H. Benetti

Publications and source records attributed to M. H. Benetti.

4 recordsLinked to original sources

arXiv2026

The Scale Invariance Behind Boltzmann Counting

Boltzmann counting possesses an exact scale invariance from which the specific entropy emerges without asymptotic approximation. Under thermodynamic replication, this invariance exposes the Gibbs excess at the multinomial level. Its resolution reveals a state-dependent scale structure whose additive refinement generates a continuum reference measure, giving a combinatorial origin to the reference structure of continuous statistical mechanics. The resulting entropy is relative to this measure, and for an ideal gas the scales acquire operational meaning through reversible work.

cond-mat.stat-mech↗

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↗