I was wondering about the hypothetical - and apparently improbable - heat death of the Universe when I stumbled upon this seeming contradiction. A certain volume of space with a uniform distribution of particles has maximum entropy. However, the action of gravity would condense these particles, decreasing the entropy of the system, which would violate the second law of thermodynamics.
My question is simply: what am I missing here? What is the solution to this contradiction?
A certain volume of space with a uniform distribution of particles has maximum entropy.
That is correct for non-interacting particles, but wrong for particles with the gravitational interaction. When gravity condenses these particles, it increases the entropy of the system, not decreases it, at least when the Jeans instability condition is satisfied.
To calculate entropy properly, you should consider the phase space volume, and the phase space is built with taking into account all interactions in the system.
