Thermal time models have been widely applied to predict temperature requirements for seed germination. Generally, a log-normal distribution for thermal time [θT(g)] is used in such models at suboptimal temperatures to examine the variation in time to germination arising from variation in θT(g) within a seed population. Recently, additional distribution functions have been used in thermal time models to predict seed germination dynamics. However, the most suitable kind of the distribution function to use in thermal time models, especially at suboptimal temperatures, has not been determined. Five distributions (log-normal, Gumbel, logistic, Weibull and log-logistic) were used in thermal time models over a range of temperatures to fit the germination data for 15 species. The results showed that a more flexible model with the log-logistic distribution, rather than the log-normal distribution, provided the best explanation of θT(g) variation in 13 species at suboptimal temperatures. Thus, at least at suboptimal temperatures, the log-logistic distribution is an appropriate candidate among the five distributions used in this study. Therefore, the distribution of parameters [θT(g)] should be considered when using thermal time models to prevent large deviations; furthermore, an appropriate equation should be selected before using such a model to make predictions.

The maximum-entropy formalism developed by E. T. Jaynes is applied to the breaking strain of a bundle of fibers of various cross-sectional areas. When the bundle is subjected to a tensile load, and it is assumed that Hooke's law applies up to the breaking strain of the fibers, it is proved that the survival strain distribution for a fiber in the bundle is restricted to a certain class consisting of generalizations of the log-logistic distribution. Since Jaynes's formalism is a generalization of statistical thermodynamics, parallels are drawn between concepts in thermodynamics and in the theory of inhomogeneous bundles of fibers. In particular, heat transfer corresponds to damage to the bundle in the form of broken fibers, and the negative reciprocal of the parameter corresponding to thermodynamic temperature is the resistance of the bundle to damage.