Abstract
In the world about us the past is distinctly different from the future. Milk spills but doesn't unspill; eggs splatter but do not unsplatter; waves break but do not unbreak; we always grow older, never younger. These processes all move in one direction in time - they are called "time-irreversible" and define the arrow of time. It is therefore very surprising that the relevant fundamental laws of nature make no such distinction between the past and the future. This in turn leads to a great puzzle - if the laws of nature permit all processes to be run backwards in time, why don't we observe them atoms and molecules, the microscopic components of material systems, give rise to the observed time-irreversible behavior of our everyday world? I will describe the resolution of this apparent paradox due to Maxwell, Thomson and (particularly) Boltzmann, in the classical setting.
I will also discuss newer developments in both the classical and quantum settings.