相关论文: Convergence to equilibrium for the discrete coagul…
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…
Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the…
The paper considers the convergence to equilibrium for measure solutions of the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. We prove the exponential sharp rate of strong convergence to equilibrium for…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
The exponential decay of the relative entropy associated to a fully discrete porous-medium equation in one space dimension is shown by means of a discrete Bakry-Emery approach. The first ingredient of the proof is an abstract discrete…
The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation, it is proved that fragmentation prevents the occurrence of…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed…
The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo-Martin-Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of open quantum…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…
The quasi--equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…
We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schr\"odinger equation with diffusive forcing.…