Recently, several authors have tried to extend the usual concepts of thermodynamics and kinetic theory in order to deal with distributions that can be non-Boltzmannian. For dissipative systems described by the canonical ensemble, this leads to the notion of nonlinear Fokker-Planck equation (T.D. Frank, Non Linear Fokker-Planck Equations, Springer, Berlin, 2005). In this paper, we review general...

The first considered problem is the problem of arising dynamic dissipative structures in the chemical reactor volume. The mathematical model of heat and mass transfer in the tubular through-reactors has been submitted. The model consists of the diffusion-kinetic equations for two reagents under the first-order reversible reaction and heat transfer equation with allowance for the latent heat of ...

We generalize Chirikov's resonance-overlap criterion for the onset of global chaos in Hamiltonian systems to describe the onset of chaotic attractors in weakly dissipative systems.

We study two specific measures of quality of chemical reaction networks, Precision and Sensitivity. The two measures arise in the study of sensory adaptation, in which the reaction network is viewed as an input-output system. Given a step change in input, Sensitivity is a measure of the magnitude of the response, while Precision is a measure of the degree to which the system returns to its orig...

We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While resulting short-time dynamics governed by non-Hermitian variants Aubry-Andr\'e-Harper model, we demonstrate how phases and phase transitions pertaining to fundamentally change long-time, steady-state-approaching under Lindblad master equ...

I will talk about the general energetic variational approaches for hydrodynamic systems of complex fluids. In these energetic variational approaches, the least action principle (LAP) with action functional gives the Hamiltonian parts (conservative force) of the hydrodynamic systems, and the maximum/minimum dissipation principle (MDP), i.e., Onsager’s principle, gives the dissipative parts (diss...