Related papers: Interacting Dynamics
We explore a two-body system with superexponential interactions that serves as a fundamental building block for a route to complexity. While being of striking simplicity this highly nonlinear interaction yields a plethora of intriguing…
We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the kind reader to consult the extended abstract in the paper.
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we…
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…
The macroscopic fluctuation theory provides a complete hydrodynamic description of non-equilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we show how to construct a microscopic open…
We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or…
It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is introduced to describe the dynamics of a system…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…
Based on local gauge invariance, four different kinds of fundamental interactions in Nature are unified in a theory which has $SU(3)_c \otimes SU(2)_L \otimes U(1) \otimes_s Gravitational Gauge Group$ gauge symmetry. In this approach,…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…