Related papers: Complexity, Entropy, and Markov Chains

A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…

In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the…

The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates…

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…

We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that…

We study the entropy of Chinese and English texts, based on characters in case of Chinese texts and based on words for both languages. Significant differences are found between the languages and between different personal styles of debating…

We study the change of multiparticle entanglement if one particle becomes classical, in the sense that this particle is destructed by a measurement, but the gained information is encoded into a new register. We present an estimation of this…

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the…

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…

We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…

We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction…

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the…

In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use…

We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…

The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…