Enropic Dynamics In Bullet Items

Entropic dynamics (ED) is a framework that is used to derive theories. Quantum theory is an example of ED. In ED, the privilege role is given to the position of particle. A system of N particles lives in a configuration space. To find the equation that describes the quantum system. First step is to define an entropy functional
S[P,Q]=-ʃ dy P(y|x)log(P(y|x)/Q(y|x))
where P(y|x) is the transition probability distribution when particle moves from initial position x to y and Q(y|x) is the prior probability distribution.
The second step is find the relevant constraints which comes in the form expected values.
The third step is to maximize the entropy functional subject to constraints.
One obtains the Fokker-Planck (FP) equation.
According to FP equation there is only one dynamical variable and that is the probability distribution.
A second degree of freedom is needed to derive quantum theory. To get that, a second constraint is needed and that is expected energy is conserved.
One obtains the Hamilton-Jacobi equation (HJE).
Combining the FPE and HJE equations one obtains the Schrodinger equation (SE) which may contain non-linear terms that describes solitons.