Susskind answered a similar question during his stat. phys. lectures which you can watch on iTunes. Somebody asked the following question: given that entropy i

Susskind answered a similar question during his stat. phys. lectures which you can watch on iTunes. Somebody asked the following question: given that entropy is the volume of the system in phase space and Liouville's Theorem (of classical physics) tells us that the volume in phase space is conserved, how come entropy increases? His answer: Liouville's Theorem holds, the volume stays the same, but the blob representing the system (the system's microstates) spreads out in a fractal way in phase space, increasing the "coarse-grained" phase volume / entropy. Then, a "you can't set the initial conditions infinitely precisely" / "you can't measure inifinitally presicely" type argument is invoked to say that in terms of real-life reversibility the course-grained volume is what matters, so entropy has increased despite Liouville. Explained here: http://www.google.com/url?sa=t&source=web&ct=res&cd=21&url=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DR-jQ4I0VkdoC%26pg%3DPA70%26lpg%3DPA70%26dq%3Dliouville%2Btheorem%2Bentropy%26source%3Dbl%26ots%3DRKI8zXfw-0%26sig%3DtZOa77uJCTs8-XibeaJWf3qhPKk%26hl%3Den%26ei%3DrquWSvulI47Y-QatkeTQCQ%26sa%3DX%26oi%3Dbook_result%26ct%3Dresult%26resnum%3D1&ei=rquWSvulI47Y-QatkeTQCQ&usg=AFQjCNGLutp18ilwZw-_ZISvOG_oxCbISw&sig2=mk0O2_FIpPZ3etOpTas28g http://www.google.com/url?sa=t&source=web&ct=res&#38...