Justification in Statistical Mechanics.

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fundamentally flawed, and will show that some puzzles sometimes associated with the second law are merely artifacts of this incorrect justification. 1 The Standard Story. If we squirt some colored ink into a closed container of moving water, we are justified in expecting that the ink will eventually disperse itself evenly through the water. Indeed, if we prepare any system in a state of low entropy, and then isolate the system, we are justified in expecting that the system will experience an increase in entropy. In virtue of what are these beliefs justified? Such beliefs can, of course, be justified on purely inductive grounds. But one might also think that such beliefs ought to be able to be justified on the basis of more fundamental physical and mathematical principles. In this paper, I would like to discus