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Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…
We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to…
We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix…
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…
Despite the increasing interest, the research field which studies the concepts of work and heat at quantum level has suffered from two main drawbacks: first, the difficulty to properly define and measure the work, heat and internal energy…
Engines are open systems that can generate work cyclically, at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
A closed expression for the density operator of the damped harmonic oscillator is extracted from the master equation based on the Lindblad theory for open quantum systems. The entropy and effective temperature of the system are subsequently…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
We consider the dynamics of a model introduced recently by Bialas, Burda and Johnston. At equilibrium the model exhibits a transition between a fluid and a condensed phase. For long evolution times the dynamics of condensation possesses a…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
The system decomposition theory has recently been developed for the dynamic analysis of nonlinear compartmental systems. The application of this theory to the ecosystem analysis has also been introduced in a separate article. Based on this…
The occupation number is a key observable for diagnosing thermalization, as it connects directly to standard statistical laws such as Fermi--Dirac, Bose--Einstein, and Boltzmann distributions. In the context of spin systems, it represents…
We introduce the concepts of closed sets and closure operators as mathematical tools for the study of social networks. Dynamic networks are represented by transformations. It is shown that under continuous change/transformation, all…