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system. Natural processes tend to make the universe more disordered.
The second law of thermodynamics tells us that, if an isolated system
undergoes a spontaneous process, its final state will be one in which the
entropy (and also P) is maximum. There is always, in principle, the

possibility that, by a statistical fluctuation, some other state might occur,
even a state whose entropy is lower than that of the initial state. For
systems with very small numbers of particles such fluctuations from

average behavior are indeed there to be seen, the Brownian motion is a
good example. For macroscopic systems, however, the probability that the
entropy will actually decrease in a spontaneous process proves to be
unbelievably small. Thus, you can predict with complete confidence that

the molecules of air in your room will not spontaneously congregate on
one side, a glass of room-temperature water will not spontaneously
separate into ice cubes and warmer water, and your, coffee will not

spontaneously begin rotating in the cup. Each of these processes can
conserve energy, and, thus, would be consistent with the first law. They
will, however, not be observed, even if you keep watching at them as long

as the present age of the universe! It has been said that calculations of
probabilities of such events give operational meaning to the word "never."

2.14 Heat Death of the Universe

The so-called notion of " Heat Death of the Universe" was
formulated by R. Clausius in 1865 on the basis of the second law of
thermodynamics. According to the second law, any physical system that

does not exchange energy with other systems (such exchange is obviously
precluded for the universe as a whole) tends toward the most probable
equilibrium state: the state of maximum entropy. Such a state would
correspond to the heat death of the universe.

Even before the development of modern cosmology, numerous
attempts were made to disprove the notion of the heat death of the
universe. The best known attempt was the fluctuation hypothesis advanced

by L. Boltzmann in 1872. According to this hypothesis, the universe is in
an isothermal equilibrium state, but, in accordance with the law of chance,
deviations from this state sometimes occur in one place or another; the

larger the region encompassed by the deviations and the greater the degree
of deviation, the less often the deviations occur.

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