Related papers: Topological Entropy Bounds for Switched Linear Sys…
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…
The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…
We establish a relation between the boundary and the topological entropies for the conformal minimal models in some of the simplest models of the unitary A-A series. We show that in these models the boundary entropy is a difference of…
This work studies how to preemptively increase the resilience of a network by means of time-varying topological actuation. To do this, we focus on linear dynamical systems that are compatible with a given network, and consider policies that…
Stirring a two-dimensional viscous fluid with rods is often an effective way to mix. The topological features of periodic rod motions give a lower bound on the topological entropy of the induced flow map, since material lines must `catch'…
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the…
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
Nonequilibrium processes break time-reversal symmetry and generate entropy. Living systems are driven out-of-equilibrium at the microscopic level of molecular motors that exploit chemical potential gradients to transduce free energy to…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multi-particle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the…
For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty.…
We study the lower bound of the entropy production in a one-dimensional underdamped Langevin system constrained by a time-dependent parabolic potential. We focus on minimizing the entropy production during transitions from a given initial…