# Fluctuation Hypothesis

## Fluctuation Hypothesis

a cosmological hypothesis advanced by L. Boltzmann. According to the fluctuation hypothesis, the entire observable galaxy, including the solar system, is a vast fluctuation in the universe, which on the whole is in a state of thermodynamic equilibrium (*see*HEAT DEATH OF THE UNIVERSE).

The extension of the second law of thermodynamics to systems on cosmological scales led to the conclusion that a final state of thermodynamic equilibrium, called the state of maximum entropy, is inevitable for such systems and, ultimately, for the entire universe. In the state of maximum entropy, no macroscopic changes or motions whatsoever would be possible, and no organized structures of any nature could exist. At the same time, however, the universe that we can observe is decidely not in such a state. The fluctuation hypothesis was proposed in 1872 as a possible explanation of this paradox. In the framework of statistical thermodynamics, the existence of nonequilibrium subsystems in an equilibrium system is possible but unlikely. According to the fluctuation hypothesis, not only small fluctuations but also vast—and all the more unlikely—fluctuations should arise in an equilibrium universe, provided the universe is sufficiently large.

The fluctuation hypothesis was the most outstanding attempt to resolve the paradox of the heat death of the universe within the framework of classical, that is, prerelativistic, physics and cosmology. However, from the standpoint of physics, the probability of a fluctuation of the necessary scale is so small and the time required for the occurrence of such a fluctuation is so great that the difference between the concepts of “unlikely” and “impossible” becomes, in essence, a formality. On the other hand, from the standpoint of a philosophy that encompasses more than just physics, the notion that the existence of life—and of organized structures in general—turns out to be almost a miracle is unsatisfactory. Thus, the paradox of the heat death of the universe is, in essence, not eliminated but only mitigated.

Like other cosmological paradoxes, the paradox of the heat death of the universe cannot be consistently resolved at all in the framework of the classical picture of the world; for, relativistic physics (in particular, relativistic thermodynamics), rather than classical physics, is applicable to phenomena that occur on a cosmological scale. In 1928 the American physicist R. Tolman showed that if gravity is taken into account, a conclusion is reached which is unexpected from the standpoint of classical thermodynamics, namely, that the entropy of a system can increase without limit without the system attaining any final state with maximum entropy. (*See also*COSMOLOGY.)

### REFERENCES

Boltzmann, L.*Stat’i i rechi*. Moscow, 1970.

Tolman, R.

*Otnositel’nost’, termodinamika i kosmologiia*. Moscow, 1974. (Translated from English.)

Zel’dovich, Ia. B., and I. D. Novikov.

*Stroenie i evoliutsiia Vselennoi*. Moscow, 1975.

G. I. NAAN