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H-FUNCTION EVOLUTION IN COLLISIONLESS SELF-GRAVITATING SYSTEMS

H-FUNCTION EVOLUTION IN COLLISIONLESS SELF-GRAVITATING SYSTEMS An expression is derived for the time derivative of a general H function in which the potential appears explicitly. As is well-known, starting at a specific time with a coarse-grained distribution function that is equal to the fine-grained distribution function, at short times later the H function is a nondecreasing function of time. In general, however, one cannot claim this for arbitrary time. The expression is applied to self-gravitating systems. The condition for having a nondecreasing H function for all coarse-grained distribution functions is that, on the average, the high-density regions contract and the low-density regions expand. An example of using the expression derived to calculate the derivative of the H function with respect to time is discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Publications of the Astronomical Society of the Pacific IOP Publishing

H-FUNCTION EVOLUTION IN COLLISIONLESS SELF-GRAVITATING SYSTEMS

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Copyright
Copyright © 1990. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.
ISSN
0004-6280
eISSN
1538-3873
DOI
10.1086/132683
Publisher site
See Article on Publisher Site

Abstract

An expression is derived for the time derivative of a general H function in which the potential appears explicitly. As is well-known, starting at a specific time with a coarse-grained distribution function that is equal to the fine-grained distribution function, at short times later the H function is a nondecreasing function of time. In general, however, one cannot claim this for arbitrary time. The expression is applied to self-gravitating systems. The condition for having a nondecreasing H function for all coarse-grained distribution functions is that, on the average, the high-density regions contract and the low-density regions expand. An example of using the expression derived to calculate the derivative of the H function with respect to time is discussed.

Journal

Publications of the Astronomical Society of the Pacific – IOP Publishing

Published: Jun 1, 1990

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