The principle of maximum entropy has recently been applied to several problems of condensed matter theory. In this paper we discuss some technical aspects of the maxent approach t o these problems, and show some general properties of the applications of the method. In particular, we show that maxent can be thought o f a s a c o n venient w ay to close hierarchies, and to extrapolate perturbation series for quantities of physical interest. An illustration of this viewpoint i s p r o vided by an

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... xamination of the dynamics of a quantum mechanical spin system. We discuss a general maxent method for the extrapolation of power series, and apply the method both to problems of condensed matter a virial equation of state and spin resonance problems, and to a classic example of a di cult series to handle: the anharmonic quantum oscillator with octic perturbation. We show that the inclusion of information beside Taylor coe cients is critical to obtaining a satisfactory extrapolation for the divergent perturbation series. A general maxent criterion is proposed for optimal series extrapolation.