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We evoke situations where large fluctuations in the entropy are induced, ourmain example being a spacetime containing a potential black hole whoseformation depends on the outcome of a quantum mechanical event. We argue thatthe teleological character of the event horizon implies that the consequententropy fluctuations must be taken seriously in any interpretation of thequantal formalism. We then indicate how the entropy can be well defined despitethe teleological character of the horizon, and we argue that this is possibleonly in the context of a spacetime or ``histories'' formulation of quantumgravity, as opposed to a canonical one, concluding that only a spacetimeformulation has the potential to compute --- from first principles and in thegeneral case --- the entropy of a black hole. From the entropy fluctuations ina related example, we also derive a condition governing the form taken by theentropy, when it is expressed as a function of the quantal density-operator.Comment: 35 pages, plain Tex, needs mathmacros.tex and msmacros.te

Large fluctuations in the horizon area and what they can tell us about entropy and quantum gravity