Change in Entropy
The action of a curve on a Riemannian manifold is given by
The path parameter here is time t; this action can be understood to give the change in entropy of a system as it is moved from time a to time b. Specifically, one has
as the change in entropy. This observation has resulted in practical applications in chemical and processing industry: in order to minimize the change in entropy of a system, one should follow the minimum geodesic path between the desired endpoints of the process. The geodesic minimizes the entropy, due to the Cauchy–Schwarz inequality, which states that the action is bounded below by the length of the curve, squared.
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Famous quotes containing the words change in, change and/or entropy:
“The attitude is we live and let live. This is actually an amazing change in values in a rather short time and it’s an example of freedom from religion.”
—Tom Wolfe (b. 1931)
“If we confine ourselves to one life role, no matter how pleasant it seems at first, we starve emotionally and psychologically. We need a change and balance in our daily lives. We need sometimes to dress up and sometimes to lie around in torn jeans. . . . Even a grimy factory can afford some relief from a grimy kitchen and vice versa.”
—Faye J. Crosby (20th century)
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)