Márcio Sampaio Gomes-Filho

arXiv2025

The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond

In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by the fluctuation-dissipation theorem (FDT). The conceptual foundation of FDT originates from the definition of the equilibrium state and Onsager's regression hypothesis. Over time, the fluctuation-dissipation relation has been vividly investigated also in systems far from equilibrium, which often exhibit wild fluctuations in measured parameters. In this review, we recall the major formulations of the FDT, including those proposed by Langevin, Onsager and Kubo. We discuss the role of fluctuations in a broad class of growth and diffusion phenomena and examine the violation of the FDT resulting from a transition from Euclidean to fractal geometry. Finally, we highlight possible generalizations of the FDT formalism and discuss situations where the relation breaks down and is no longer applicable.

cond-mat.stat-mech↗

arXiv2023

Modeling the diffusion-erosion crossover dynamics in drug release

A computational model is proposed to investigate drug delivery systems in which erosion and diffusion mechanisms are participating in the drug release process. Our approach allowed us to analytically estimate the crossover point between those mechanisms through the value of the parameter $b$ ($b_c = 1$) and the scaling behavior of parameter $τ$ on the Weibull function, $\exp[-(t/τ)^b]$, used to adjust drug release data in pharmaceutical literature. Numerical investigations on the size dependence of the characteristic release time $τ$ found it to satisfy either linear or quadratic scaling relations on either erosive or diffusive regimes. Along the crossover the characteristic time scales with the average coefficient observed on the extreme regimes ({\it i.e.}, $τ\sim L^{3/2}$), and we show that this result can be derived analytically by assuming an Arrhenius relation for the diffusion coefficient inside the capsule. Based on these relations a phenomenological expression for the characteristic release in terms of size $L$ and erosion rate $κ$ is proposed, which can be useful for predicting the crossover erosion rate $κ_c$. We applied this relation to the experimental literature data for the release of acetaminophen immersed in a wax matrix and found them to be consistent with our numerical results.

cond-mat.stat-mech↗