Requiring the entropic dynamics of a probability density and phase to preserve both symplectic and information-geometric structures yields the linear Schrödinger equation.
Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics
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abstract
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.
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The Entropic Dynamics approach to Quantum Mechanics
Requiring the entropic dynamics of a probability density and phase to preserve both symplectic and information-geometric structures yields the linear Schrödinger equation.