Related papers: Quasistatic dynamical systems
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time.…
The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition…
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
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…
We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given…
We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only…
We present results on a series of 2D atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…