Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0404111

Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model

Martin Depken·Robin Stinchcombe
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analytically study a one dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a $1/\ln t$ fashion. The response and correlation functions turn out to be connected through a non-equilibrium generalisation of the fluctuation-dissipation theorem. The initial response in the average density to an increase in the tapping strength is shown to be negative, while on longer timescales it is shown to be positive. On short time scales the fluctuation-dissipation theorem governs the relation between correlation and response, and we show that such a relationship also exists for the slow degrees of freedom, albeit with a different temperature. The model is further studied within the statistical theory proposed by Edwards and co-workers, and the Edwards entropy is calculated in the large system limit. The fluctuations described by this approach turn out to match the fluctuations as calculated through the dynamical consideration. We believe this to be the first time these ideas have been analytically confirmed in a non-mean-field model.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Martin Depken, Robin Stinchcombe. 2005-08-04. Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model. https://doi.org/10.1103/physreve.71.065102

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification using X-rays and binary alloys appears well within the existing techniques, while feasibility for neutron scattering requires further study. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

cond-mat.stat-mech↗
arXiv2026

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble

We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form $ω^{2}=k^{2}+4E_{*}^{-1/2}k^{5/2}$, where $E_{*}$ sets the characteristic scale of the multifractional correction. Working within the grand-canonical ensemble, we derive the modified density of states, the grand potential, the partition function, and the main thermodynamic quantities for both bosonic and fermionic sectors. The deformation changes the available phase-space distribution and produces nonstandard thermal scalings controlled by the ratio $T/E_{*}$. In the infrared regime, the usual relativistic gas behavior is recovered with leading corrections proportional to powers of $(T/E_{*})^{1/2}$. In the ultraviolet regime, the density of states scales as $\varrho(ω)\propto ω^{7/5}$, corresponding to an effective density-of-states dimension $d_{\mathrm{eff}}=12/5$. As a consequence, the Stefan-Boltzmann law is deformed from $u\propto T^{4}$ to $u\propto E_{*}^{3/5}T^{17/5}$, while the equation-of-state parameter approaches $w=5/12$ instead of the standard radiation value $w=1/3$. We also analyze thermal stability, particle number and energy fluctuations, Bose-Einstein condensation, and the degenerate Fermi gas limit. The multifractional correction increases the critical temperature of a conserved bosonic gas and modifies the Fermi energy, pressure, sound speed, and low-temperature heat capacity of degenerate fermions. A direct fit to the COBE/FIRAS monopole spectrum yields $E_{*}>0.36\,\mathrm{MeV}$ at $95\%$ CL, while the conservative GWTC--3 propagation constraint gives $E_{*}>1.18\times10^{19}\,\mathrm{GeV}$ at $90\%$ credibility when the dispersion relation is assumed to be universal.

cond-mat.stat-mech↗
arXiv2026

Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory

We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.

cond-mat.stat-mech↗