534 research outputs found
Quantum Entanglement and Entropy
Entanglement is the fundamental quantum property behind the now popular field
of quantum transport of information. This quantum property is incompatible with
the separation of a single system into two uncorrelated subsystems.
Consequently, it does not require the use of an additive form of entropy. We
discuss the problem of the choice of the most convenient entropy indicator,
focusing our attention on a system of 2 qubits, and on a special set, denoted
by . This set contains both the maximally and the partially entangled
states that are described by density matrices diagonal in the Bell basis set.
We select this set for the main purpose of making more straightforward our work
of analysis. As a matter of fact, we find that in general the conventional von
Neumann entropy is not a monotonic function of the entanglement strength. This
means that the von Neumann entropy is not a reliable indicator of the departure
from the condition of maximum entanglement. We study the behavior of a form of
non-additive entropy, made popular by the 1988 work by Tsallis. We show that in
the set , implying the key condition of non-vanishing entanglement, this
non-additive entropy indicator turns out to be a strictly monotonic function of
the strength of the entanglement, if entropy indexes larger than a critical
value are adopted. We argue that this might be a consequence of the
non-additive nature of the Tsallis entropy, implying that the world is quantum
and that uncorrelated subsystems do not exist.Comment: 27 pages, 0 figure
Collective behavior and evolutionary games - An introduction
This is an introduction to the special issue titled "Collective behavior and
evolutionary games" that is in the making at Chaos, Solitons & Fractals. The
term collective behavior covers many different phenomena in nature and society.
From bird flocks and fish swarms to social movements and herding effects, it is
the lack of a central planner that makes the spontaneous emergence of sometimes
beautifully ordered and seemingly meticulously designed behavior all the more
sensational and intriguing. The goal of the special issue is to attract
submissions that identify unifying principles that describe the essential
aspects of collective behavior, and which thus allow for a better
interpretation and foster the understanding of the complexity arising in such
systems. As the title of the special issue suggests, the later may come from
the realm of evolutionary games, but this is certainly not a necessity, neither
for this special issue, and certainly not in general. Interdisciplinary work on
all aspects of collective behavior, regardless of background and motivation,
and including synchronization and human cognition, is very welcome.Comment: 6 two-column pages, 1 figure; accepted for publication in Chaos,
Solitons & Fractals [the special issue is available at
http://www.sciencedirect.com/science/journal/09600779/56
Towards the timely detection of toxicants
We address the problem of enhancing the sensitivity of biosensors to the
influence of toxicants, with an entropy method of analysis, denoted as
CASSANDRA, recently invented for the specific purpose of studying
non-stationary time series. We study the specific case where the toxicant is
tetrodotoxin. This is a very poisonous substance that yields an abrupt drop of
the rate of spike production at t approximatively 170 minutes when the
concentration of toxicant is 4 nanomoles. The CASSANDRA algorithm reveals the
influence of toxicants thirty minutes prior to the drop in rate at a
concentration of toxicant equal to 2 nanomoles. We argue that the success of
this method of analysis rests on the adoption of a new perspective of
complexity, interpreted as a condition intermediate between the dynamic and the
thermodynamic state.Comment: 6 pages and 3 figures. Accepted for publication in the special issue
of Chaos Solitons and Fractal dedicated to the conference "Non-stationary
Time Series: A Theoretical, Computational and Practical Challenge", Center
for Nonlinear Science at University of North Texas, from October 13 to
October 19, 2002, Denton, TX (USA
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