Directional complexity and entropy for lift mappings

We introduce and study the notion of a directional complexity and entropy for maps of degree 1 on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a combinatorial machinery to obtain exact formulas for the directional entropy, to find the maximal directional entropy, and to show that it equals the topological entropy of the map. Keywords: Rotation interval, Space-time window, Directional complexity, Directional entropy;Comment: 19p. 3 fig, Discrete and Continuous Dynamical Systems-B (Vol. 20, No. 10) December 201

OTOC, complexity and entropy in bi-partite systems

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure

Threshold Effects and Lorentz Symmetry

Evidence on the violation of Lorentz symmetry arises from the observation of cosmic rays with energies beyond the GZK cutoff, $E_{GZK} \simeq 4 \times 10^{19} eV$, from the apparent transparency of the Universe to the propagation of high energy gamma radiation and from the stability of pions in air showers. These three paradoxes can be explained through deformations of the relativistic dispersion relation. Theoretical ideas aimed to understand how Lorentz symmetry may be broken and phenomenologically interesting deformations of the relativistic dispersion relation may arise are briefly discussed.Comment: 7 pages. Talk presented at the ``Decoherence, Information, Complexity and Entropy 2002'', Piombino, Italy, September 200

Complexity Science in Human Change: Research, Models, Clinical Applications

Complexity and entropy prevail in human behavior and social interaction because the systems underlying behavior and interaction are, without a doubt, highly complex [...

About the Importance of Interface Complexity and Entropy for Online Information Sharing

In this paper, we describe two experiments that show the powerful influence of interface complexity and entropy on online information sharing behaviour. 134 participants were asked to do a creativity test and answer six open questions against three different screen backgrounds of increasing complexity. Our data shows that, as an interface becomes more complex and has more entropy users refer less to themselves and show less information sharing breadth. However, their verbal creativity and information sharing depth do not suffer in the same way. Instead, an inverse U shaped relationship between Interface complexity and creativity as well as information sharing depth can be observed: Users become more creative and thoughtful until a certain tipping point of interface complexity is reached. At that point, creativity and th inking suffer, leading to significantly less disclosure. This result challenges the general HCI assumption that simplicity is always best for computers interface design , as users'creativity and information sharing depth initially increases with more interface complexity. Our results suggest that the Yerkes Dodson Law may be a key theory underlying online creativity and depth of online disclosures

Quantum Zeno Effect in the Decoherent Histories

The quantum Zeno effect arises due to frequent observation. That implies the existence of some experimenter and its interaction with the system. In this contribution, we examine what happens for a closed system if one considers a quantum Zeno type of question, namely: "what is the probability of a system, remaining always in a particular subspace". This has implications to the arrival time problem that is also discussed. We employ the decoherent histories approach to quantum theory, as this is the better developed formulation of closed system quantum mechanics, and in particular, dealing with questions that involve time in a non-trivial way. We get a very restrictive decoherence condition, that implies that even if we do introduce an environment, there will be very few cases that we can assign probabilities to these histories, but in those cases, the quantum Zeno effect is still present.Comment: 7 pages, To appear in DICE 2006 (Decoherence Information Complexity and Entropy) conference proceeding