Universe has more entropy than thought

For all its tumult — erupting stars, colliding galaxies, collapsing black holes — the cosmos is a surprisingly orderly place. Theoretical calculations have long shown that the entropy of the universe — a measure of its disorder — is but a tiny fraction of the maximum allowable amount.

A new calculation of entropy upholds that general result but suggests that the universe is messier than scientists had thought — and slightly further along on its gradual journey to death, two Australian cosmologists conclude.

An analysis by Chas Egan of the Australian National University in Canberra and Charles Lineweaver of the University of New South Wales in Sydney indicates that the collective entropy of all the supermassive black holes at the centers of galaxies is about 100 times higher than previously calculated. Because supermassive black holes are the largest contributor to cosmic entropy, the finding suggests that the entropy of the universe is also about 100 times larger than previous estimates, the researchers reported online September 23 at arXiv.org.

Entropy quantifies the number of different microscopic states that a physical system can have while looking the same on a large scale. For instance, an omelet has higher entropy than an egg because there are more ways for the molecules of an omelet to rearrange themselves and still remain an omelet than for an egg, notes cosmologist Sean Carroll of the California Institute of Technology in Pasadena.

A black hole is the entropy champ because there are myriad ways for all the material that has fallen into it to be arranged microscopically while the black hole retains the same numerical values for its observable properties — charge, mass and spin.

Researchers who previously calculated the cosmic sum of black hole entropy had assumed that, on average, each galaxy houses a 10 million solar-mass black hole at its center. Under this assumption, researchers had determined that supermassive black holes contribute an entropy of about 10¹⁰², in units derived from a quantity known as Boltzmann’s constant.
 
In contrast, Egan and Lineweaver relied on new data that included a fuller range of the masses of supermassive black holes rather than just using the average mass. “The upshot was that much more entropy is contributed by a smaller population of much larger, 1-billion-solar-mass black holes,” Egan says.

Carroll says that the team’s calculation looks sensible. “I see no reason to doubt their numbers,” he says.

Having a more reliable entropy estimate is important, says Egan, because for life or other complex phenomena to exist, the entropy of the universe must be less than the maximum possible value. Consider, he notes, when hot water is poured into a cold bath. Initially the hot and cold water are separate and the system is orderly — it has low entropy. But once the hot and cold water are thoroughly mixed, the entropy is maximized and no further heat flow is possible.

In the case of the universe, Egan says, “we’d like to know [when and] if the entropy will eventually reach a maximum value, marking the end of all dissipative processes, including life.” Physicists have dubbed that maximum entropy “heat death.”

Egan and Lineweaver’s new value for the entropy of the universe is still a billionth of a billionth the maximum possible entropy that researchers have estimated. Nonetheless, the new value “indicates that that the universe is a bit closer to the heat death than previously computed,” comments theorist Paul Davies of Arizona State University in Tempe.

Not everyone agrees that the higher entropy contributed by supermassive black holes puts the universe closer to heat death. Theorist Ned Wright of the University of California, Los Angeles says that because the extra entropy is locked inside the black holes, the rest of the universe should have lower entropy and be further away from heat death.     

The new entropy calculation also highlights a cosmic puzzle, Carroll says. The entropy was relatively small in the early universe (10⁸⁸), bigger now (10¹⁰⁴), but still falls far short of the maximum (10¹²²). No known physical principle can explain why the cosmic entropy is so low. But it’s a good thing because the low value “is responsible for everything we experience about the [unidirectional] flow of time — breaking eggs, growing older and dying, remembering the past but not the future,” notes Carroll. “The universe is incredibly more orderly than it has any right to be. Egan and Lineweaver have shown that it’s just a bit more disorderly than we thought.”