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    Volume 2, Number 1 - May 1956

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    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

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    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

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    We carry out a thorough survey of entropy for a large class of pp-branes in various dimensions. We find that the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic pp-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic pp-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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