Related papers: The Smoluchowski Ensemble: Statistical Mechanics o…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Size-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, generalized sensitivity functions (GSFs)…
The multicomponent coagulation equation is a generalisation of the Smoluchowski coagulation equation in which size of a particle is described by a vector. As with the original Smoluchowski equation, the multicomponent coagulation equation…
Smoluchowski's coagulation equation is a mean-field model describing the growth of clusters by successive mergers. Since its derivation in 1916 it has been studied by several authors, using deterministic and stochastic approaches, with a…
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…
At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature,…
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j} = i^{\nu}j^{\mu} + j^{\nu}i^{\mu}$ homogeneous in masses $i$ and $j$ of…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal…
Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples of a physical system's equilibrium density. The equilibrium distribution is…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
In a recent series of papers, an exact combinatorial solution was claimed for a variant of the so-called Marcus--Lushnikov model of aggregation. In this model, a finite number of aggregates, are initially assumed to be present in the form…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…
We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system is consists of clusters of various masses whose concentrations evolve according to an…
In this work, we prove a two-scale homogenization result for a set of diffusion-coagulation Smoluchowski-type equations with transmission boundary conditions. This system is meant to describe the aggregation and diffusion of pathological…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of conserved quantities $\pi$, generalising the multiplicative kernel. For these kernels, a…
The properties of statistical ensembles with abelian charges close to the thermodynamic limit are discussed. The finite volume corrections to the probability distributions and particle density moments are calculated. Results are obtained…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…