We introduce a class of translation-invariant measures on the set {0, …, q−1}ℤ determined by a set of q d-dimensional matrices. They are algebraic in the sense that their densities are obtained by applying a functional to products of the defining matrices. Positivity of probabilities is assured by assuming a positivity structure on the algebra of defining matrices. Restricting attention to the usual positivity notion of positive matrix elements, a detailed analysis leads to a canonical representation theorem that solves the parametrization problem. Furthermore, we show that the class of algebraic measures coincides with the class of functions of Markov processes with finite state spaces. Our main result consists in the detailed study of the asymptotics of the conditional probabilities from which we derive a formula for the mean entropy.

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Germinating spores of Mucor rouxii rapidly broke down their large (23% of the dry weight) trehalose reserve. More than 50% of this trehalose was broken down to ethanol. About one‐third of the trehalose was converted to glycerol, which started to leak out of the spores after some 20 min germination. The synthesis of glycerol was not associated with any major change in glycerol 3‐phosphatase activity in the spores. Since its rate of leaking was much smaller and the internal concentration reached was much higher in spores subjected to osmotic stress, glycerol might play a role in the initial water uptake and swelling of the germinating spores.

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