Previously, the ubiquitous issue regarding severe wasting of computational resources in all forms of molecular simulations due to repetitive local sampling was raised, and the local free energy landscape approach was proposed to address it. This approach is derived from a simple idea of first learning local distributions, and followed by dynamic assembly of which to infer global joint distribution of a target molecular system. When compared with conventional explicit solvent molecular dynamics simulations, a simple and approximate implementation of this theory in protein structural refinement harvested acceleration of about six orders of magnitude without loss of accuracy. While this initial test revealed tremendous benefits for addressing repetitive local sampling, there are some implicit assumptions need to be articulated. Here, I present a more thorough discussion of repetitive local sampling; potential options for learning local distributions; a more general formulation with potential extension to simulation of near equilibrium molecular systems; generalization of repetitive local sampling to repetitive local computation and potential application in accelerating numerical solving of complex equations; the prospect of developing computation driven molecular science; and the connection to mainstream residue pair distance distribution based protein structure prediction/refinement. This more general development is termed the local distribution theory to release the limitation of strict thermodynamic equilibrium in its potential wide application in both soft condensed molecular systems and complex equations.