http://imechanica.org/taxonomy/term/1055 Comments for "entropy" en http://imechanica.org/node/1563#comment-3128 <p> Another way to look at this question... </p> <p> Is the discrete probability theory at all necessary here? Of course, Boltzmann used it, but I think it should not be absolutely necessary. ... To see how, you may think in terms of the Fourier analysis of diffusion. The time evolution in diffusion leads to a loss&nbsp;of the&nbsp;sharpness&nbsp;initially present in the signal. ... This fact, viz., that diffusion smoothens out any sharpness, is what corresponds to&nbsp;the increase&nbsp;in entropy. A discussion in terms of particles is just one way to describe the situation. </p> <p> As an aside: For a continuum description, only the Fourier theory--a non-local theory--has been generally available so far. However, a *local* continuum theory *is*, of course, possible. This is an interesting issue by itself... </p> <p> Coming back to the main discussion thread: The second law&nbsp;really is marvellous. No matter what formalism you use, what terms, you simply can&#39;t escape the basic physical fact denoted by&nbsp;it. </p> <p> ----- </p> <p> Another matter.&nbsp;I am not sure if the current MD simulation technology is at all capable of showing any melting in the first place... Could someone clarify this matter, please? Is the theory of MD sufficiently well developed that quantum mechanical calculations&nbsp;done on an initial&nbsp;solid state of a material would invariably *lead* to a change of state to the liquid state in the simulation? How about the solids like camphor that directly vaporize? (This would be a test case, really speaking!) </p> <br class="clear" /> Sat, 16 Jun 2007 09:45:18 -0400 Ajit R. Jadhav comment 3128 at http://imechanica.org