Changes

The fact that this kind of heat flow is irreversible makes the whole field of thermodyamics lie outside of the realm of classical Newtonian mechanics or Relativistic mechanics.  In Newtonian or Relativistic mechanics, every phenomenon can go in reverse order.  The catchy phrase "arrow of time" (or "time's arrow") was coined by [[Arthur Eddington]] to denote this one-way behavior not shared by other theories of physics.<ref>''The Nature of the Physical World'', Arthur Eddington, MacMillan, 1929, ISBN 0-8414-3885-4</ref>

The fact that this kind of heat flow is irreversible makes the whole field of thermodyamics lie outside of the realm of classical Newtonian mechanics or Relativistic mechanics.  In Newtonian or Relativistic mechanics, every phenomenon can go in reverse order.  The catchy phrase "arrow of time" (or "time's arrow") was coined by [[Arthur Eddington]] to denote this one-way behavior not shared by other theories of physics.<ref>''The Nature of the Physical World'', Arthur Eddington, MacMillan, 1929, ISBN 0-8414-3885-4</ref>

Where does the magic of the second law come from?  It comes from the field of statistical mechanics, which is the study of the behavior of huge aggregates of particles, typically at the molecular or atomic level.  While Newtonian and Relativistic mechanics can, in principle, precisely describe assemblages of any number of particles, in practice they are not directly applied to the behavior of bulk material.  That is, they are not applied to a number of particles on the order of Avogadro's number.

Prior to the insight of [[quantum mechanics]], which established the fundamental underlying uncertainty in the universe, the field of statistical mechanics attributed the increase in entropy to the statistical tendencies of huge aggregates of particles at the molecular or atomic level.  While Newtonian and Relativistic mechanics can, in principle, precisely describe assemblages of any number of particles, in practice they are not directly applied to the behavior of bulk material.  That is, they are not applied to a number of particles on the order of Avogadro's number.

It is not useful to think of the seeming randomness of statistical mechanics as arising from the randomness ([[Heisenberg Uncertainty Principle]]) of [[Quantum Mechanics]].  Statistical mechanics was developed in the 19^th century, long before Quantum Mechanics.  It does not depend on the deep philosophical uncertainty of Quantum Mechanics; it is the study of the ''completely deterministic'' behavior of an assemblage of molecules of not-precisely-known initial state.

Statistical mechanics was developed in the 19^th century prior to quantum mechanics, so rather than attributing the Second Law to the fundamental uncertainty in nature, statistical mechanics bases its models on assumptions concerning the statistical behavior of large numbers of particles.

==Probability and statistics==

==Probability and statistics==