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We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…
Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time…
This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in non-Noetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Modeling and simulation of complex systems is key to explore systems dynamics. Many scientific approaches were developed to represent dynamic structure systems but most of these approaches are efficient for some kinds of systems and…
One of the most important goals in quantum thermodynamics is to demonstrate advantages of thermodynamic protocols over their classical counterparts. For that, it is necessary to (i) develop theoretical tools and experimental set-ups to deal…
Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many…
A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions…
An iterative scheme is presented to solve analytically the relativistic fluid dynamics equations. The scheme is applied to longitudinal expansion, transversal symmetric and transversal asymmetric (triaxial) expansion as well. Within this…
Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
We characterize locally injective semialgebraic maps between two semialgebraic sets in terms of the induced homomorphism between their rings of (continuous) semialgebraic functions.
We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the…