Abstract
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.
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