Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0508557

A Nonequilibrium Thermodynamic Approach to Generalized Statistics for Brownian Motion

I. Santamaria-Holek·R. F. Rodriguez
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyze the dynamics of a Brownian gas in contact with a heat bath in which large temperature fluctuations occur. There are two distinct time scales present, one describes the decay of the fluctuations in the temperature and the other one is associated with the establishment of local equilibrium. Although the gas has reached local equilibrium, there exist large fluctuations in an intensive parameter (temperature) which break the thermodynamic equilibrium with the heat bath. Thus the decay of the fluctuations in the intensive parameter is larger than the characteristic time for the establishment of local equilibrium. We show that the dynamics of such large and intensive fluctuations may be described by adopting a nonequilibrium thermodynamics approach with an adequate formulation of local equilibrium. A coarsening procedure is then used to contract the space of mesoscopic variables needed to describe the dynamics of the gas and the extensive character of the description is lost. This procedure allows us to derive an effective Maxwell-Boltzmann factor (EMBF) for the Brownian gas, as has been recently proposed in the literature. Furthermore, we use this local equilibrium distribution and an entropy functional to derive a nonequilibrium probability distribution and a hydrodynamic description for the Brownian gas which contains fluctuating transport coefficients. The ensuing description is nonextensive and our analysis shows that the coarse-graining procedure is responsible for the nonextensivity property.

Explore related subjects

cond-mat.stat-mechcond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

I. Santamaria-Holek, R. F. Rodriguez. 2005-09-29. A Nonequilibrium Thermodynamic Approach to Generalized Statistics for Brownian Motion. https://doi.org/10.1016/j.physa.2005.10.009

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

KEEP EXPLORING

Related papers

arXiv2026

A General Solution for Network Models with Pairwise Edge Coupling

Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous results obtained for specific interaction structures. We use the Hubbard-Stratonovich transform to show that such higher order models can be decoupled into families of effectively separable random graph models, which might be enhanced with auxiliary, possibly multi-valued, parameters identifying the thermodynamical phase of the system. Moreover, given the diagonalizability of couplings between links, we carry out the full computation of the partition functions and discuss why in some cases they can effectively reduce to the one for the Mean-Field case.

cond-mat.stat-mech↗
arXiv2026

Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations

We develop a dynamic theory of eikonal attenuation and mutual coherence for a quantum particle propagating through equilibrium Coulomb fluctuations. The one-particle length $\ell$ is the attenuation length of the ensemble-averaged retarded propagator, not an Anderson localization length or a transport mean free path. For a collisionless classical one-component plasma (OCP), the potential spectrum follows from the fluctuation--dissipation theorem and the RPA dielectric function. In suitable plasma parameter windows, both fast and slow probe regimes are physically meaningful. Fast probes recover the Coulomb logarithm with the dynamical infrared length $v/ω_{\rm p}$. Slow probes yield $G(v)\propto v$ and, in the controlled weak branch, $\ell\propto k$. We derive an exact finite-thickness mutual-coherence expression and a closed slow-regime transverse scaling function. Within the controlled slow-OCP and thick-slab window, the logarithmic two-ray visibility scales as $v^{-1}$ at fixed transverse separation, in contrast to the $v^{-2}$ dependence for frozen finite-slab fluctuations. For a symmetric diffusive electrolyte, linearized stochastic density functional theory gives the exact on-shell result $G_{\rm el}(v)=(m^2C/\hbar^4)\operatorname{arsinh}[v/(2Dκ)]$, where $C=k_{\mathrm B}Tq_0^2/(4π\varepsilon_b)$. For ordinary liquid electrolytes, the slow diffusive limit is inaccessible within the spatial eikonal regime and is therefore a formal asymptote. The physically relevant electrolyte limit is instead that of a fast probe, $v\gg Dκ$, where the diffusive charge relaxation generates an intrinsic infrared length $v/(Dκ^2)$ absent from the quasi-static theory.

cond-mat.stat-mech↗
arXiv2026

Planckian dissipation from classical hydrodynamics

Hydrodynamics describes the long-time, long-distance dynamics of interacting quantum systems by classical equations, yet at low temperature quantum fluctuations might eventually invalidate this classical picture. Here we ask what it takes for a quantum system to sustain a consistently classical hydrodynamic description. Our starting point is the quantum fluctuation-dissipation theorem which, when read in the time domain, acts as a blurring of the fine details of correlation functions on a Planckian time-scale. We analyse how this blurring interacts with the diffusive large-deviation form of correlators assuming the existence of a hydrodynamic light cone velocity, and show that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. We illustrate the mechanism on three phenomenological hydrodynamic equations - diffusion, telegraph and diffusive-telegraph. Preserving a finite classical region as the temperature is lowered forces the current relaxation rate to be bounded from above by the Planckian rate. This bound connects to bounds on diffusivity, equilibration time and shear viscosity. In this way, a Planckian bound on dissipation emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.

cond-mat.stat-mech↗