I am suggesting browsing the the following site http://en.wikipedia.org/wiki/Entropy for more information about entropy and its relation to the unidirectional arrow of time. Then we can continue discussion on the part that remains unclear.
__________________ Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c˛