arXiv subjects

Samuel M. Soares

Publications and source records attributed to Samuel M. Soares.

4 recordsLinked to original sources

arXiv2026

Hyperstatistics

We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain analytical closed-form expressions for the here proposed $(q, n)$-generalized Boltzmann factor $B^n_q$ considering uniform, $γ$, Log-normal, F, and the $q$-$γ$ probability distribution functions. Remarkably, for all investigated distribution functions, $B^n_q$ reduces to a $q$-exponential-type function. To demonstrate the applicability of hyperstatistics, we use a table top experiment of the discharge of a capacitor considering $γ$-distributed relaxation times, the pressure decay over time associated with the pumping of $^4$He lines of a closed cycle cryostat, midrapidity data for $p$-Pb collisions at the LHC, as well as data set for acceleration distribution in turbulent systems. Furthermore, we deduce the power-law-like dielectric response using the $q$-$γ$-distribution function. Our proposal is applicable to systems with inherent non-Boltzmann-Gibbsian statistics in domains of the system.

cond-mat.stat-mech↗

arXiv2026

A few remarks on hyperstatistics and some applications

In a recent paper [arXiv:2604.24783 (2026)], we have proposed a general approach to treat systems with inherent non-Boltzmann-Gibbsian behaviour. Given the extremely high accuracy of our approach, we have adopted the term hyperstatistics. We have applied such a statistical mechanics approach, i.e., hyperstatistics, to the discharge of a capacitor in a RC series circuit, pumping of $^4$He of a closed cycle cryostat, midrapidity data of $p$-Pb collisions at the LHC, as well as for the distribution of accelerations in turbulent systems. Here, we discuss into more details the ground of hyperstatistics. We demonstrate the versatility of hyperstatistics upon applying it to the velocity autocorrelation function in Brownian motion and also regarding its potential to describe brain dynamics.

cond-mat.stat-mech↗

arXiv2026

Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem

Critical phenomena have been extensively investigated both theoretically and experimentally in many fields, such as condensed matter physics, biology, e.g., brain criticality, and cosmology. In particular, the behaviour of response functions right at critical points (CPs) is highly topical. It turns out that in the frame of Boltzmann-Gibbs-von Neumann-Shannon approach, the extensive character of entropy breaks down at CPs. The latter implies diverging susceptibilities, which is at odds with experimental observations. Here, we investigate the influence of the spin magnitude $S$ on the quantum Grüneisen parameter $Γ^{0\text{K}}_{q}$ right at CPs for the 1D Ising model under a transverse magnetic field. Our findings are fourfold: $\textit{i}$) for higher $S$, $Γ^{0\text{K}}_{q}$ is increased, but remains finite, reflecting the enhancement of the Hilbert space dimensionality; $\textit{ii}$) the Schmidt decomposition theorem recovers the extensivity of the nonadditive $q$-entropy $S_q$ only for a $\textit{special}$ value of the entropic index $q$; $\textit{iii}$) the universality class in the frame of $S_q$ depends only on the symmetry of the system; $\textit{iv}$) we propose an experimental setup to explore finite-size effects in connection with the Hilbert space occupation at CPs. Our findings unveil both universal and non-universal aspects of quantum criticality in terms of $Γ^{0\text{K}}_{q}$ and $S_q$.

quant-ph↗

arXiv2024

Universally non-diverging Grüneisen parameter at critical points

According to Boltzmann-Gibbs (BG) statistical mechanics, the thermodynamic response, such as the isothermal susceptibility, at critical points (CPs) presents a divergent-like behavior. An appropriate parameter to probe both classical and quantum CPs is the so-called Grüneisen ratio $Γ$. Motivated by the results reported in Phys. Rev. B $\textbf{108}$, L140403 (2023), we extend the quantum version of $Γ$ to the non-additive $q$-entropy $S_q$. Our findings indicate that using $S_q$ at the unique value of $q$ restoring the extensivity of the entropy, $Γ$ is universally non-diverging at CPs. We unprecedentedly introduce $Γ$ in terms of $S_q$, being BG recovered for $q \rightarrow 1$. We thus solve a long-standing problem related to the $\textit{illusory}$ diverging susceptibilities at CPs.

cond-mat.stat-mech↗