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We investigate the efficiency of several types of continued fractionexpansions of a number in the unit interval using a generalization of Lochstheorem from 1964. Thus, we aimed to compare the efficiency by describing therate at which the digits of one number-theoretic expansion determine those ofanother. We study Chan's continued fractions, $\theta$-expansions,$N$-continued fractions and R\'enyi-type continued fractions. A central role infulfilling our goal is played by the entropy of the absolutely continuousinvariant probability measures of the associated dynamical systems.

A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms