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We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…
We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no…
We investigate an ideal gas in a time--dependent external trapping potential. We use the Boltzmann equation with the relaxation time ansatz to explore the time--dependent energy of an adiabatically isolated system. In particular we are…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
In this contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion in general and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
How does a driven system with many energy levels approach its steady state? Insights are gained by studying a system with three energy levels when the ground state is excited by a laser. The time-dependent occupation probabilities of the…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…
We consider nonequilibrium (NEQ) states such as supercooled liquids and glasses that are described with use of internal variables. We classify the latter by state-dependent hierarchy of relaxation times to assess their relevance for…
We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method.…
By suitable reformulations, we review the mathematical frameworks of six different approaches to the description of non-equilibrium dynamics with the purpose to set up a unified formulation of the Maximum Entropy Production (MEP) principle…
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling…