An Entropy Maximum Principle and Relaxation Phenomena.
NAVAL RESEARCH LAB WASHINGTON DC
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A Shannon epoch entropy is defined in terms of an integral over the full temporal epoch of relaxation. A maximum entropy principle yields a linear exponential as a fundamental form for relaxation to equilibrium. It is observed that the time scale of measurements does not in general coincide with the time scale on which the fundamental form is described. Time scale transformations are considered. The maximum entropy density is taken to be form-invariant independent of the time scale used in its description, and the resulting epoch entropy is itself taken to be an invariant. This latter invariance leads to a relation between the time unit on a transformed time scale and the time unit on the fundamental scale. An appropriate choice for the form of a time scale of measurements for relaxation phenomena is rationalized. The results of the complete formalism are a fractional exponential for relaxation decay, and renormalization relations for scaling parameters and activation energies. These results have been consistently verified in a wide range of relaxation measurements for many kinds of condensed matter. Author
- Statistics and Probability