Chapter 9: Fundamental Physics

Section 3: Irreversibility and the Second Law of Thermodynamics

Current thinking on the Second Law

The vast majority of current physics textbooks imply that the Second Law is well established, though with surprising regularity they say that detailed arguments for it are beyond their scope. More specialized articles tend to admit that the origins of the Second Law remain mysterious. Most ultimately attribute its validity to unknown constraints on initial conditions or measurements, though some appeal to external perturbations, to cosmology or to unknown features of quantum mechanics.

An argument for the Second Law from around 1900, still reproduced in many textbooks, is that if a system is ergodic then it will visit all its possible states, and the vast majority of these will look random. But only very special kinds of systems are in fact ergodic, and even in such systems, the time necessary to visit a significant fraction of all possible states is astronomically long. Another argument for the Second Law, arising from work in the 1930s and 1940s, particularly on systems of hard spheres, is based on the notion of instability with respect to small changes in initial conditions. The argument suffers however from the same difficulties as the ones for chaos theory discussed in Chapter 6 and does not in the end explain in any real way the origins of randomness, or the observed validity of the Second Law.

With the Second Law accepted as a general principle, there is confusion about why systems in nature have not all dissipated into complete randomness. And often the rather absurd claim is made that all the order we see in the universe must just be a fluctuation—leaving little explanatory power for principles such as the Second Law.

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From Stephen Wolfram: A New Kind of Science [citation]