Electronic Resource
Springer
Journal of statistical physics
24 (1981), S. 325-343
ISSN:
1572-9613
Keywords:
Entropy
;
dynamical system
;
K-system
;
H-theorem
;
irreversibility
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the timet. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal. Under suitable conditions (which are stated explicitly) this entropy approaches the equilibrium entropy ast→+∞ and the fine-grained entropy ast→−∞. In particular, the conditions can always be satisfied if the system is aK-system, as in the Sinai billiard models. Some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition, and at the same time elucidate the connection between our concept of entropy and the entropy invariant of Kolmogorov and Sinai.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01013304
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