Related papers: Entropy Flexibility of Dynamical Systems
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological…
Controversy exists regarding the possible existence of a transition between the liquid and glassy states of water. Here we use experimental measurements of the entropy, specific heat, and enthalpy of both liquid and glassy water to…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and computed in a variety of examples. In…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion…
This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their…
We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of…
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution…
We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and…
Three topics in dynamical systems are discussed. In the first two sections we solve some open problems concerning, respectively, Furstenberg entropy of stationary dynamical systems, and uniformly rigid actions admitting a weakly mixing…