3 research outputs found
Correlation in states of two identical particles
We identify the correlation in a state of two identical particles as the
residual information beyond what is already contained in the 1-particle reduced
density matrix, and propose a correlation measure based on the maximum entropy
principle. We obtain the analytical results of the correlation measure, which
make it computable for arbitrary two-particle states. We also show that the
degrees of correlation in the same two-particle states with different particle
types will decrease in the following order: bosons, fermions, and
distinguishable particles.Comment: 3.6 page
Quantifying structure in networks
We investigate exponential families of random graph distributions as a
framework for systematic quantification of structure in networks. In this paper
we restrict ourselves to undirected unlabeled graphs. For these graphs, the
counts of subgraphs with no more than k links are a sufficient statistics for
the exponential families of graphs with interactions between at most k links.
In this framework we investigate the dependencies between several observables
commonly used to quantify structure in networks, such as the degree
distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure
How should complexity scale with system size?
We study how statistical complexity depends on the system size and how the complexity of the whole system relates to the complexity of its subsystems. We study this size dependence for two well-known complexity measures, the excess entropy of Grassberger and the neural complexity introduced by Tononi, Sporns and Edelman. We compare these results to properties of complexity measures that one might wish to impose when seeking an axiomatic characterization. It turns out that those two measures do not satisfy all those requirements, but a renormalized version of the TSE-complexity behaves reasonably well. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200889.75.-k Complex systems, 89.70.+c Information theory and communication theory,