Coarse Graining and the Second Law of Thermodynamics

[Fraser]

Hi all, first post so be nice :)

I'm currently taking a statistical physics course and I am very confused about an aspect relating to the second law.

Currently we are considering a member of an ensemble to be represented by a moving point in phase space (a 6N dimensional space spanned by Pi and qi from Hamiltonian). My notes for this show that a point in this space represents a microstate of the assembly. I can just about accept this.

I have been presented with a full derivation for Liovilles equation (which I follow) and this has shown that the density of representative points are constant with time. From the classical definition of Gibbs Entropy this leads to the entropy change with time equal to 0. I follow the maths for this ok, which is fine.

What I don't understand is the idea of coarse graining that follows this. My notes say that by averaging the density of phase space over a fixed local scale we can increase S. But why is this? Surely all we have done is 'drop' some information about the ensemble and therefore force S to increase? But how is this right? How can we just forget about some particles and therefore say the entropy has increased? Surely this means that we CAN'T consider particles as an incompressible fluid since the second law isn't obeyed when we do this?

Thanks in advance,

Fraser

 

[Drakkith]

I think it is saying that IF the particles were all spread out, the entropy would increase. If you just average the density then the actual entropy isn't increasing, but it would if that actually happened. Thats what it looks like to me at least.