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Development of Statistical mechanics methods

Statistical mechanics methods developed. a) Staged Particle deletion method for the evaluation of the chemical potential b) Direct particle deletion method for the evaluation of the chemical potential c) Enrichment of ensemble average in any Markovian chain by including all possible outcomes of any trial moves (either performed in the chain sampling of the chain or even if it is a “ghost” move) with the extension of performing parallel Monte Carlo moves. (Named Integration over a Marvokian Web) d) Dynamical exploration of “glassy” landscapes via stochastic expansion of the explored landscapes. (Named Dynamical Integration over a Marvokian Web) e) Temperature accelerates rate constant calculations based on multiple histogram reweighing of a “swan” of Molecular Dynamics microcanonical trajectories. f) Combination of the multiple histogram reweighing method with the Gibbs Ensemble method. g) Direct free energy evaluation via the deletion of all the particles in the system.

Development of fundamental theory.

a) An integral form of the First order Free energy Perturbation theory that allows the direct removal of molecules. b) The theory behind the Integration over a Markovian Web that enables the combination of dynamical and static sampling in Markovian chains, the enrichment of ensemble average via “ghost” Monte Carlo moves. c) Extension of the mean first passage time theory for the development of the Dynamical Integration over a Marvokian Web method. d) Representation of both Observables and probability in a common Euclidian space: Provides a geometrical representation of statistic and statistical mechanics and provides a geometrical representation of the experimental observed dynamical relaxation modes. e) Free energy perturbation in the form of Non-Equilibrium Work relations and vise -versa