Uniformity, Non-Uniformity, and Irreversibility

We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, ...

 Life as "Improbable Distribution of Molecules"

At the end of the last century Boltzman made an elegant redefinition of entropy as a measure of the probability of a molecular distribution. It may seem at first obscure, but it leads directly to what we seek. It implies that the probably life or one of its products, and if we find such a distribution to be global in extent then perhaps we are seeing something of Gaia, the largest living creature on Earth. But what, you may ask, is an improbable distribution of molecules? There are many poss...