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Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The challenge is to specify how those constraints are themselves updated.

The important ingredients are two: the cotangent bundle associated to the probability simplex inherits (1) a natural symplectic structure from ED, and (2) a natural metric structure from information geometry.

The requirement that the dynamics preserves both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow) leads to a Hamiltonian dynamics of probabilities in which the linearity of the Schrödinger equation, the emergence of a complex structure, Hilbert spaces, and the Born rule, are derived rather than postulated.


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