Letters

Still more faces of entropy

"Another Face of Entropy" (SN: 8/15/98, p. 108) was the best explanation of entropy that I have ever read. I have always wondered if the compressed matter in a black hole is at a very low state of entropy. If so, could the creation and growth of very large numbers of black holes overcome the laws of thermodynamics?

Donald C. Wilfong
San Ramon, Calif.

Black holes actually contain the most entropy possible in a given space, theorists say. Jacob Bekenstein and Steven Hawking concluded in the mid-1970s that the entropy of a black hole is proportional to the area of a disk surrounding it from within which matter or energy cannot escape. According to physicist Lee Smolin, in his book The Life of the Cosmos (1997, Oxford University Press), a consequence of that finding is that the maximum entropy of a given region of space is the entropy of the largest black hole that can fit into it.

—P. Weiss

In some entropic self-assembly experiments, virus particles were used; however, it is not stated that such particles carry electric charge. Thus, the result is not a pure entropy effect associated with the geometry and kinetics of the particles involved.

Frank Meno
Pittsburgh, Pa.

To minimize the influence of electrostatic forces among the viruses and other colloidal particles, experimenters add salts to their suspensions. Salt ions form clouds around each colloidal particle that cause the particles to appear neutrally charged within a limited range of distance from each other.

—P. Weiss

Have any of the "entropy force" researchers considered the implications of their work for cosmology? The "uniform" soup that cosmologists assume for the first instants of the universe is obviously a low-entropy, highly unstable situation. As soon as the first phase transition—the separation of photons and solid matter—occurs, entropy takes over. Photons, being smaller than the resultant helium atoms, will start shoving the atoms around until they coalesce and expand into the soap bubble structures we see in the universe today.

Tim LeGore
West Richland, Wash.

Would this view of entropy explain the self-organization of the early universe? It occurs to me that in the time between the inflation of the universe and the phase change when the energy density dropped to the point of transparency, the environment was perfect for the kind of "organization by entropy" that this article discusses. If the principles and behavior apply at the appropriate scale, then this phenomenon could provide the impetus to define the structure that we now see in the universe.

In fact, the timescale is sufficient for the creation of massive gravity wells. It may well be that entropy is responsible for organizing the

structures, up to and including galaxies and galactic clusters, even before the "phase change" to a "transparent" universe. If this were the case, then there would be no need for any more esoteric mechanism to explain it.

William Lightner
Rogers, Ark.

Entropic forces similar to those that organize particles in colloidal suspensions most likely played little, if any, role in the organization of the early universe, physicists contend. The density of primordial particles was far too low to allow the constant jostling among particles that leads to entropy-driven order. Cosmologists also see no parallel between galaxy-galaxy collisions, in which galaxies typically mingle and deform, and the hard body versus hard body, purely repulsive encounters of entropy-ruled systems. At that galactic scale, they say gravity appears to be the dominant force.

—P. Weiss

How about entropy playing a role in the deposition of plaque in blood vessels? Could depletion forces contribute to this phenomenon?

Bob McClintock
Miami, Fla.

It occurred to me that the entropy experiments might provide another computational verification of the problem raised in "Cracking Kepler's sphere-packing problem" (SN: 8/15/98, p. 103). A large number of big balls and a larger number of small balls would be placed in a container. After allowing time for interaction, the packing of clusters of the big balls far from the container walls would simply be observed.

Several prerequisite questions would need to be answered to prove the approach viable. Does maximizing the restricted regions of overlap of the big balls equate to maximum entropy? Does maximizing those restricted regions equate to tightest packing of the big balls? And what experimental conditions allow the system to reach a global entropy maximum without getting stuck in some local maximum? I suspect that choosing ball sizes that guarantee no overlap of nearby restricted regions can help in answering yes to the first two questions.

Wendell Bishop
Somerville, Mass.

Chickadee choices

In "Chickadees sneak up the social ladder" (SN: 7/11/98, p. 27), self-selection and a desire to improve the breed may not be the controlling factors as the wayward female chickadee sneaks up the social ladder. She probably has no alternative. Males ranking below her spouse would be quite unwilling to mate and risk his wrath.

J. William Newitt
Flemington, N.J.

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