Universal geometric approach to uncertainty, entropy, and information

Universal geometric approach to uncertainty, entropy and information

It is shown that a unique measure of volume is associated with any statistical ensemble, which directly quantifies the inherent spread or localisation of the ensemble. It is applicable whether the ensemble is classical or quantum, continuous or discrete, and may be derived from a small number of theory-independent geometric postulates. Remarkably, this unique ensemble volume is proportional to ...

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A Geometric Approach to Universal Quasigroup Identities

In the present paper we construct the accompanying identity ^ I of a given quasigroup identity I. After that we deduce the main result: I is isotopically invariant (i.e., for every guasigroup Q it holds that if I is satissed in Q then I is satissed in every quasigroup isotopic to Q) if and only if it is equivalent to ^

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A Geometric Approach to Universal Quasigroup

In the present paper we construct the accompanying identity ^ I of a given quasigroup identity I. After that we deduce the main result: I is isotopically invariant (i.e., for every guasigroup Q it holds that if I is satissed in Q then I is satissed in every quasigroup isotopic to Q) if and only if it is equivalent to ^

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Volume of classical and quantum ensembles: geometric approach to entropy and information

It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a “volume”. This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It further provides a simple geometric picture for deriving and unifying a number of results in classical and quantum information theory, and for discussing entro...

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