相关论文: How far is complex balancing from detailed balanci…

We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…

Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…

In this paper, we provide a detailed theoretical analysis of the numerical scheme introduced in J. Comput. Phys. 436 (2021) 110253 for the reaction kinetics of a class of chemical reaction networks that satisfies detailed balance condition.…

The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…

In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's master equation)…

Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…

Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…

This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…

The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…

In a recent Letter [Phys.Rev.Lett., 77,4536 (1996), chao-dyn/9609014] Altland and Zirnbauer claim that they rigorously proved the complete analogy between a (classically chaotic) dynamical system and disordered (random) solids. The purpose…

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…

Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems…

Can a micron sized sack of interacting molecules understand, and adapt to a constantly-fluctuating environment? Cellular life provides an existence proof in the affirmative, but the principles that allow for life's existence are far from…

This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms…

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo-Martin-Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of open quantum…

We study a connection between quantum detailed balance, which is a concept of importance in statistical mechanics, and entanglement. We also explore how this connection fits into thermofield dynamics.

While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…

Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review…