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Volume 2, Number 1 - May 1956
The Entropy (also published as the Providence College Journal of Physics and Chemistry) was an undergraduate scholarship journal published by the Phi Chi Club of Providence College. (Volume 2, Number 1 - May 1956 - 16 pages in total.
Entropy of gravitating systems: scaling laws versus radial profiles
Through the consideration of spherically symmetric gravitating systems
consisting of perfect fluids with linear equation of state constrained to be in
a finite volume, an account is given of the properties of entropy at conditions
in which it is no longer an extensive quantity (it does not scale with system's
size). To accomplish this, the methods introduced by Oppenheim [1] to
characterize non-extensivity are used, suitably generalized to the case of
gravitating systems subject to an external pressure. In particular when, far
from the system's Schwarzschild limit, both area scaling for conventional
entropy and inverse radius law for the temperature set in (i.e. the same
properties of the corresponding black hole thermodynamical quantities), the
entropy profile is found to behave like 1/r, being r the area radius inside the
system. In such circumstances thus entropy heavily resides in internal layers,
in opposition to what happens when area scaling is gained while approaching the
Schwarzschild mass, in which case conventional entropy lies at the surface of
the system. The information content of these systems, even if it globally
scales like the area, is then stored in the whole volume, instead of packed on
the boundary.Comment: 16 pages, 11 figures. v2: addition of some references; the stability
of equilibrium configurations is readdresse
Entropy of Near-Extremal Black p-branes
We carry out a thorough survey of entropy for a large class of -branes in
various dimensions. We find that the Bekenstein-Hawking entropy may be given a
simple world volume interpretation only for the non-dilatonic -branes, those
with the dilaton constant throughout spacetime. The entropy of extremal
non-dilatonic -branes is non-vanishing only for the solutions preserving 1/8
of the original supersymmetries. Upon toroidal compactification these reduce to
dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6
dimensions, which preserves 1/4 of the original supersymmetries, the
near-extremal entropy is found to agree with a world sheet calculation, in
support of the existing literature. The remaining 3 interesting cases preserve
1/2 of the original supersymmetries. These are the self-dual 3-brane in 10
dimensions, and the 2- and 5-branes in 11 dimensions. For all of them the
scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking
temperature is in agreement with a statistical description in terms of free
massless fields on the world volume.Comment: 16 pages, harvmac; improved discussion of M-theory charge
quantization (version to appear in Nucl. Phys. B
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