Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
The trick is that Boltzmann assumed that a gas (a discrete set of interacting molecules) can be considered as a continuum of points and, on top of that, that the particles can be considered independent of each other: if these arbitrary assumptions are dropped, no rigorous proof for the irreversibility of natural processes exists.
The French mathematician Jules Henri Poincaré (“Sur le problème des trois corps et les équations de la dynamique”, 1890), for example, proved just about the opposite: that every closed system must eventually revert in time to its initial state (the “recurrence theorem”). Thus everything that can happen “will” happen, and will happen infinite times. Poincaré proved eternal recurrence where Thermodynamics had just proved eternal doom. The German mathematician Ernst Zermelo immediately (“On a Theorem of Dynamics and the Mechanical Theory of Heat”, 1896) noticed that this would violate the law of entropy, as the return to a previous state would imply that entropy at some point must decrease in order to return to its original value.
Boltzmann could find only one rational reply: that there might be universes in which entropy decreases to compensate for universes like ours in which entropy can never decrease.
It took the Belgian (but Russian-born) physicist and Nobel-prize winner Ilya Prigogine, in the 1970s, to provide a more credible explanation for the origin of irreversibility. He observed some inherent time asymmetry in chaotic processes at the microscopic level, which would cause entropy at the macroscopic level. He reached the intriguing conclusion that irreversibility originates from randomness which is inherent in nature.
Boltzmann’s reformulation of the second law was probabilistic: it explained the entropy of the system as a property about a population of particles, not just one particle. The second law does not claim that every single particle is subject to it, but that closed systems (made of many particles) are subject to it. An individual particle may well be violating the second law for a few microseconds, but the millions of particles that make up a system will obey it (just like one person might win at the roulette once, but that episode does not change the statistical law that people lose money at the roulette). In 2002 Australian researchers, in fact, showed that microscopic systems may spontaneously become more orderly for short periods of time.
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