arXiv subjects

Lucas Squillante

Publications and source records attributed to Lucas Squillante.

16 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

The Grüneisen parameter applied to critical phenomena and experimental investigations of correlated phenomena in molecular conductors

In this Ph.D. Thesis, a systematic review is performed on the derivation and generalization of the Grüneisen parameter followed by its unprecedented applications to several distinct scenarios, such as magnetic model systems, zero-field quantum phase transitions, the maximization of caloric effects close to any critical-end point based on entropy arguments, the here-proposed adiabatic magnetization of a paramagnetic salt, as well as for Cosmology in the frame of the universe expansion. Since this Ph.D. Thesis is a symbiosis between theoretical and experimental results, an experimental investigation of correlated phenomena was carried out for molecular conductors of the (TMTTF)$_2$X family, where TMTTF is the base molecule tetramethyltetrathiafulvalene and X a monovalent counter-anion such as PF$_6$, SbF$_6$, or AsF$_6$. Such strongly correlated electron systems are considered suitable ones for the exploration of Mott insulating phase, charge-ordering, spin-Peierls, and superconductivity. In particular, the investigation of a possible multiferroic character in these salts was performed via quasi-static (low-frequency) dielectric constant $\varepsilon'$ measurements as a function of temperature where a maximum in $\varepsilon'$ as a function of temperature was observed at the corresponding charge-ordering temperature for both hydrogenated and 97.5% deuterated (TMTTF)$_2$SbF$_6$ salts. Furthermore, Raman measurements were performed on the 97.5% deuterated (TMTTF)$_2$PF$_6$, showing a possible magneto-optical effect on the $ν_4(a_g)$ vibrational mode of the TMTTF molecule. Yet, fluorescence measurements demonstrated that the fully-hydrogenated (TMTTF)$_2$AsF$_6$ presents an expressive fluorescence background, which is roughly five orders of magnitude lower than that for the 97.5% deuterated variant of (TMTTF)$_2$PF$_6$.

cond-mat.str-el↗

arXiv2024

Unveiling the interdisciplinary character of negative pressure

We explore the concept of negative pressure and its relevance in a variety of physical contexts: the expansion of the universe, mixture theory, cavitation, and the capillary effect in plants. Using thermodynamic arguments, we discuss the intricate connection between negative pressure and negative thermal expansion. We highlight the fact that metastable states and competing phases are often associated with the emergence of negative pressure. We also propose a new link between the effective Grüneisen parameter and nucleation theory.

cond-mat.stat-mech↗

arXiv2024

Higgs-like stiffness and fractons on the verge of phase transitions

In condensed matter Physics, massive longitudinal Higgs modes emerge from fluctuations of the order parameter. A few years ago, the Higgs mode was \emph{caught} experimentally in the vicinity of an insulator-to-superconductor quantum phase transition [Nat. Phys. $\textbf{11}$, 188 (2015)]. Here, we propose, in analogy to the Higgs mode, the concept of Higgs-like stiffness (HLS), which emerges close to both classical and quantum phase transitions as a universal manifestation of matter. We build up a Landau free energy for the dielectric response function to demonstrate that \emph{any} complex physical quantity can be used to infer the presence of the HLS. Our analysis is corroborated by experimental results of the quasi-static dielectric constant for the (TMTTF)$_2$SbF$_6$ Fabre salt. Yet, we discuss the appearance of fractons in connection with the locking of particular molecular rotational degrees of freedom.

cond-mat.str-el↗

arXiv2024

Cellular Griffiths-like phase

Protein compartmentalization in the frame of a liquid-liquid phase separation is a key mechanism to optimize spatiotemporal control of biological systems. Such a compartmentalization process reduces the intrinsic noise in protein concentration due to stochasticity in gene expression. Employing Flory-Huggins solution theory, Avramov/Casalini's model, and the Grüneisen parameter, we unprecedentedly propose a cellular Griffiths-like phase (CGLP), which can impact its functionality and self-organization. The here-proposed CGLP is key ranging from the understanding of primary organisms' evolution to the treatment of diseases. Our findings pave the way for an alternative Biophysics approach to investigate coacervation processes.

physics.bio-ph↗

arXiv2024

Exploring the expansion of the universe using the Grüneisen parameter

For a perfect fluid, pressure $p$ and energy density $ρ$ are related via the equation of state (EOS) $ω= p/ρ$, where $ω$ is the EOS parameter, being its interpretation usually constrained to a numerical value for each universe era. Here, based on the Mie-Grüneisen EOS, we show that $ω$ is recognized as the effective Grüneisen parameter $Γ_{eff}$, whose singular contribution, the so-called Grüneisen ratio $Γ$, quantifies the barocaloric effect. Our analysis suggests that the negative $p$ associated with dark-energy implies a metastable state and that in the dark-energy-dominated era $ω$ is time-dependent, which reinforces recent proposals of a time-dependent cosmological constant. Furthermore, we demonstrate that $Γ_{eff}$ is embodied in the energy-momentum stress tensor in the Einstein field equations, enabling us to analyse, in the frame of an imperfect fluid picture, anisotropic effects of the universe expansion. We propose that upon going from decelerated- to accelerated-expansion, a phase transition-like behavior can be inferred. Yet, our analysis in terms of entropy, $Γ$, and a by us adapted version of Avramov/Casalini's model to Cosmology unveil hidden aspects related to the expansion of the universe. Our findings pave the way to interpret cosmological phenomena in connection with concepts of condensed matter Physics via $Γ_{eff}$.

gr-qc↗

arXiv2024

Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem

The Grüneisen ratio $Γ$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic $Γ$ cannot be employed. We propose a quantum analogue to $Γ$ that computes entanglement as a function of a tuning parameter $λ$ and show that QPTs take place only for systems in which the ground-state energy depends on $λ$ non-linearly. Furthermore, we demonstrate the breakdown of the Hellmann-Feynman theorem in the thermodynamic limit at any QCP. We showcase our approach using the quantum 1D Ising model with transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the "creation of mass" close to any QCP/QPT is also discussed.

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↗

arXiv2020

Giant caloric effects close to $any$ critical end point

The electrocaloric effect (ECE), i.e., the reversible temperature change due to the adiabatic variation of the electric field, is of great interest due to its potential technological applications. Based on entropy arguments, we present a new framework to attain giant ECE. Our findings are fourfold: $i$) we employ the recently-proposed electric Grüneisen parameter $Γ_E$ to quantify the ECE and discuss its advantages over the existing so-called electrocaloric strength; $ii$) prediction of giant caloric effects $close$ to $any$ critical end point; $iii$) proposal of potential key-ingredients to enhance the ECE; $iv$) demonstration of $Γ_E$ as a proper parameter to probe quantum ferroelectricity in connection with the celebrated Barrett's formula. Our findings enable us to interpret the recently-reported large ECE at room-temperature in oxide multilayer capacitors [Nature 575, 468 (2019)], paving thus the way for new venues in the field.

cond-mat.mtrl-sci↗

arXiv2020

Griffiths-like phase close to the Mott transition

We explore the coexistence region in the vicinity of the Mott critical end point employing a compressible cell spin-$1/2$ Ising-like model. We analyze the case for the spin-liquid candidate $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, where close to the Mott critical end point metallic puddles coexist with an insulating ferroelectric phase. Our results are fourfold: $i$) a universal divergent-like behavior of the Grüneisen parameter upon crossing the first-order transition line; $ii$) based on scaling arguments, we show that within the coexistence region, for $any$ system close to the critical point, the relaxation time is entropy-dependent; $iii$) we propose the electric Grüneisen parameter $Γ_E$, which quantifies the electrocaloric effect; $iv$) we identify the metallic/insulating coexistence region as an electronic Griffiths-like phase. Our findings suggest that $Γ_E$ governs the dielectric response close to the critical point and that an electronic Griffiths-like phase emerges in the coexistence region.

cond-mat.str-el↗

arXiv2020

Epidemics, the Ising-model and percolation theory: a comprehensive review focussed on Covid-19

We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin $S$ = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis reinforces well-established literature results, namely: \emph{i}) that the epidemic curves can be described by a Gaussian-type function; \emph{ii}) that the temporal evolution of the accumulative number of infections and fatalities follow a logistic function, which has some resemblance with a distorted Fermi-Dirac-like function; \emph{iii}) the key role played by the quarantine to block the spread of Covid-19 in terms of an \emph{interacting} parameter, which emulates the contact between infected and non-infected people. Furthermore, in the frame of elementary percolation theory, we show that: \emph{i}) the percolation probability can be associated with the probability of a person being infected with Covid-19; \emph{ii}) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing, impacting thus in the probability of an infected person to infect other people. Increasing the number of infected people leads to an increase in the number of net connections, giving rise thus to a higher probability of new infections (percolation). We demonstrate the importance of social distancing in preventing the spread of Covid-19 in a pedagogical way. Given the impossibility of making a precise forecast of the disease spread, we highlight the importance of taking into account additional factors, such as climate changes and urbanization, in the mathematical description of epidemics. Yet, we make a connection between the standard mathematical models employed in epidemics and well-established concepts in condensed matter Physics, such as the Fermi gas and the Landau Fermi-liquid picture.

q-bio.PE↗

arXiv2020

Unveiling the Physics of the Mutual Interactions in Paramagnets

In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field $B_{loc}$. Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields $B$. Nevertheless, as both the temperature $T \rightarrow$ 0K and $B \rightarrow$ 0T, such many-body contributions become ubiquitous. Here, employing the magnetic Grüneisen parameter $Γ_{mag}$ and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-$T$ and vanishing $B$. Our key results are: $i$) absence of a genuine zero-field quantum phase transition due to the presence of $B_{loc}$; $ii$) connection between the canonical definition of temperature and $Γ_{mag}$; and $iii$) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions.

cond-mat.str-el↗

arXiv2019

The Magnetic Grüneisen Parameter for Model Systems

The magneto-caloric effect (MCE), which is the refrigeration based on the variation of the magnetic entropy, is of great interest in both technological applications and fundamental research. The MCE is quantified by the magnetic Grüneisen parameter $Γ_{\textmd{mag}}$. We report on an analysis of $Γ_{\textmd{mag}}$ for the classical Brillouin-like paramagnet, for a modified Brillouin function taking into account a zero-field splitting originated from the spin-orbit (SO) interaction and for the one-dimensional Ising (1DI) model under longitudinal field. For both Brillouin-like model with SO interaction and the longitudinal 1DI model, for $ T \rightarrow$ 0 and vanishing field a sign change of the MCE is observed, suggestive of a quantum phase transition. SO interaction leads to a narrowing of the critical fluctuations upon approaching the critical point. Our findings emphasize the relevance of $Γ_{\textmd{mag}}$ for exploring critical points. Also, we show that the Brillouin model with and without SO interaction can be recovered from the 1DI model in the regime of high-temperatures and vanishing coupling constant $J$.

cond-mat.str-el↗

arXiv2018

Probing the Ionic Dielectric Constant Contribution in the Ferroelectric Phase of the Fabre-Salts

In strongly correlated organic materials it has been pointed out that charge-ordering could also achieve electronic ferroelectricity at the same critical temperature $T_{co}$. A prototype of such phenomenon are the quasi-one dimensional (TMTTF)$_2X$ Fabre-salts. However, the stabilization of a long-range ferroelectric ground-state below $T_{co}$ requires the break of inversion symmetry, which should be accompanied by a lattice deformation. In this work we investigate the role of the monovalent counter-anion $X$ in such mechanism. For this purpose, we measured the quasi-static dielectric constant along the $c^{*}$-axis direction, where layers formed by donors and anions alternate. Our findings show that the ionic charge contribution is three orders of magnitude lower than the intra-stack electronic response. The $c^{*}$ dielectric constant ($ε'_{c^*}$) probes directly the charge response of the monovalent anion $X$, since the anion mobility in the structure should help to stabilize the ferroelectric ground-state. Furthermore, our $ε'_{c^*}$ measurements %conjugated with earlier investigations of the $c^*$ lattice thermal expansion, show that the dielectric response is thermally broaden below $T_{co}$ if the ferroelectric transition occurs in the temperature range where the anion movement begin to freeze in their methyl groups cavity. In the extreme case of the PF$_6$-H$_{12}$ salt, where $T_{co}$ occurs at the freezing point, a relaxor-type ferroelectricity is observed. Also, because of the slow kinetics of the anion sub-lattice, global hysteresis effects and reduction of the charge response upon successive cycling are observed. In this context, we propose that anions control the order-disorder or relaxation character of the ferroelectric transition of the Fabre-salts.

cond-mat.str-el↗