The scaling of entanglement entropy is computationally studied in several $1le d le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d =1)$ and $d=2$ rectangular lattices
with a subsystem of $L^d$ sites, the entanglement entropy associated with a {sl single} PC is found to be generically $S sim L$. We argue that the $O(L)$ entropy is an expression of the subdominant $O(L)$ entropy of the bulk entropy-area law. For $d=2$ (square) lattices connected by $m$ PCs, the area law is found to be $S sim aL^{d-1} + b m log{L}$ and is thus consistent with the anomalous area law for free fermions ($S sim L log{L}$) as $m rightarrow L$. For the Bethe lattice, the relevance of this result to Density Matrix Renormalization Group (DMRG) schemes for interacting fermions is discussed.
In the United States electoral system, a candidate is elected indirectly by winning a majority of electoral votes cast by individual states, the election usually being decided by the votes cast by a small number of swing states where the two candidat
es historically have roughly equal probabilities of winning. The effective value of a swing state in deciding the election is determined not only by the number of its electoral votes but by the frequency of its appearance in the set of winning partitions of the electoral college. Since the electoral vote values of swing states are not identical, the presence or absence of a state in a winning partition is generally correlated with the frequency of appearance of other states and, hence, their effective values. We quantify the effective value of states by an {sl electoral susceptibility}, $chi_j$, the variation of the winning probability with the cost of changing the probability of winning state $j$. We study $chi_j$ for realistic data accumulated for the 2012 U.S. presidential election and for a simple model with a Zipfs law type distribution of electoral votes. In the latter model we show that the susceptibility for small states is largest in one-sided electoral contests and smallest in close contests. We draw an analogy to models of entropically driven interactions in poly-disperse colloidal solutions.
