arXiv subjects

Henrique S. Lima

Publications and source records attributed to Henrique S. Lima.

4 recordsLinked to original sources

arXiv2026

Emergent heavy-tailed distributions from a Markovian random walk

The emergence of heavy-tailed statistics in complex systems is conventionally attributed to non-local stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a strictly local, discrete-time Markovian mechanism. The step length is governed by a deterministic function of the walker's position, establishing a positive feedback loop that induces strong effective correlations along the trajectories. Through analytical derivations in the continuum limit and extensive numerical simulations, we show that this rule yields a robust, non-Gaussian stationary state. The exact analytical solution is obtained in the closed form of a symmetric, Lorentz-like distribution, $ρ_{\text{st}}(x) \propto (|x|/l+rΔx)^{-2}$, confirming asymptotic power-law tails that decay as $|x|^{-2}$ over six decades. Furthermore, by employing the Onsager-Machlup path-integral formalism, we demonstrate that effective velocity and acceleration acquire physical meaning along the shortest fluctuation trajectories. Crucially, we find that a non-zero initial acceleration acts as the fundamental mechanism driving the walker away from the origin, ensuring both the emergence of scale-free statistics and the normalizability of the stationary distribution. This minimal pathway provides a new microscopic foundation for the widespread $-2$ power law observed across multidisciplinary complex systems.

cond-mat.stat-mech↗

arXiv2026

Superstatistical Approach to Turbulent Circulation Fluctuations

Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular interest here is the observation that circulation probability distribution functions admit a superstatistical representation, namely a description based on "ensembles of Boltzmann-Gibbs ensembles". A fundamental phenomenological ingredient of this approach, which serves as a natural starting point for modeling, relies on the strong correlation between the dissipation field and the spatial distribution of elementary circulation-carrying structures, i.e., small-scale vortices. Within the language of superstatistics, this corresponds to characterizing circulation statistics through an appropriate choice of conditioned (Boltzmann-like) distributions and mixing distributions. We show that the superstatistical class of q-exponentials, known to have broad applicability in a wide range of multiscale and non-equilibrium systems, provides an accurate description of the observed circulation statistics in homogeneous and isotropic turbulence. This finding opens avenues for exploring the statistical structure of the turbulent cascade in the context of non-extensive statistical mechanics, rooted in the concept of non-additive entropies.

physics.flu-dyn↗

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↗