Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time series context. We use this theory to derive the...

We consider some formulations of the entropy bounds at the semiclassical level. The entropy S(V ) localized in a region V is divergent in quantum field theory (QFT). Instead of it we focus on the mutual information I(V,W ) = S(V ) + S(W ) − S(V ∪W ) between two different non-intersecting sets V and W . This is a low energy quantity, independent of the regularization scheme. In addition, the mut...

Considerable interest has recently been expressed in the entropy versus area relationship for “dirty” black holes — black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = kAH/(4l 2 P ). For example, t...

Carncgie-Mellon University, Schenley Park, Pittsburgh, Pcnnsylvania 15213 Abstract Asscmhly tasks require thc fccding, acquisition. oricntation, and lnating of parts subject to contact forccs. Positional entropy providcs s n cfficicnt tool for dcscribing an asscmhly task and its ysteln impic~ncntation i n terms of the uncertainty in position and oricntation of parts as the assembly scqucncc pro...

We report measurements of the action associated with center vortices in SU(2) pure lattice gauge theory. In the lattice units the excess of the action on the plaquettes belonging to the vortex is approximately a constant, independent on the lattice spacing a. Therefore the action of the center vortex is of order A/a, where A is its area. Since the area A is known to scale in the physical units,...

Relative entropy is an essential tool in quantum information theory. There are so many problems which are related to relative entropy. In this article, the optimal values which are defined by max U∈U(Xd) S(UρU∗ ‖ σ) and min U∈U(Xd) S(UρU∗ ‖ σ) for two positive definite operators ρ, σ ∈ Pd(X ) are obtained. And the set of S(UρU∗ ‖ σ) for every unitary operator U is full of the interval [ min U∈U...

The standard approach of counting the number of eigenmodes of N scalar fields near the horizon is used as a basis to provide a simple statistical mechanical derivation of the black hole entropy in two and four dimensions. The Bekenstein formula S = A 4Gh̄ and the two-dimensional entropy S = 2M/λh̄ are naturally obtained (up to a numerical constant of order 1). This approach provides an explanatio...

One can increase one-quarter the area of a black hole, A/4, to exceed the total thermodynamic entropy, S, by surrounding the hole with a perfectly reflecting shell and adiabatically squeezing it inward. A/4 can be made to exceed S by a factor of order unity before the shell enters the Planck regime, though practical limitations are much more restrictive. One interpretation is that the black hol...