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)
“One cannot long remain so absorbed in contemplation of emptiness without being increasingly attracted to it. In vain one bestows on it the name of infinity; this does not change its nature. When one feels such pleasure in non- existence, one’s inclination can be completely satisfied only by completely ceasing to exist.”
—Emile Durkheim (1858–1917)
“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)