A Geometrical Manifold of Entropy for Fisher Information and Quantum Potential

Details A Geometrical Manifold of Entropy for Fisher Information and Quantum Potential A Geometrical Manifold of Entropy for Fisher Information and Quantum Potential

2011-10-10

arxiv.org/abs/1110.5491v1

Physics

Quantum Physics

16 pages

Scientific paper

It is here proposed a geometric approach for the problem of describing entropy in a quantum system. We make use of an extension of tensor calculus called morphogenetic calculus. By using such formalism we express the entropy of a quantum system as the superposition of Boltzmann entropies. In this way we also provide a reading of the relational interpretation of quantum mechanics. Moreover we show that the Bohm quantum potential emerges as a consequence of the classical equilibrium under the constraint of a minimum condition of Fisher information. In this way, Bohm quantum potential appears as a non-Euclidean deformation of the probabilistic space. Finally we investigate the possible quantum-relativistic extensions of the theory and the connections with the problem of quantum gravity.

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