Abstract: A method and system thereof for simulating behavior of a thermodynamic system over time, including a momentum refreshment process and a conservative dynamics process, where the momentum refreshment process includes partially refreshing a momentum to define refreshed momentum by considering solutions for a starting momentum determined by a numerical implementation for integrating a generating linear differential equation.

Abstract: A method of simulating behaviour of a molecular system with m degrees of freedom over time comprising a partial momentum refreshment step and a molecular dynamics step, wherein the partial momentum refreshment step comprises: given a starting position q and a starting momentum p of the molecular system, partially refreshing the momentum to define refreshed momentum p? evaluating the shadow Hamiltonian 331 ?t at position q and momentum p?; and accepting or rejecting the refreshed momentum p? according to a Metropolis-type function and if p? is accepted using p? as the resulting momentum p and starting position q as the resulting position q or if it is rejected, using p as the resulting momentum p and starting position q as the resulting position; and wherein the molecular dynamics step comprises: given a starting position q and starting momentum p of the molecular system, running a molecular dynamics simulation over a fixed number of iterations and obtaining new position q? and new momentum p?; evaluating the

Abstract: A method and system thereof for simulating behaviour of a thermodynamic system over time, including a momentum refreshment process and a conservative dynamics process, where the momentum refreshment process includes partially refreshing a momentum to define refreshed momentum by considering solutions for a starting momentum determined by a numerical implementation for integrating a generating linear differential equation.

Abstract: A method of simulating behaviour of a molecular system with m degrees of freedom over time comprising a partial momentum refreshment step and a molecular dynamics step, wherein the partial momentum refreshment step comprises: given a starting position q and a starting momentum p of the molecular system, partially refreshing the momentum to define refreshed momentum p? evaluating the shadow Hamiltonian at position q and momentum p?; and accepting or rejecting the refreshed momentum p? according to a Metropolis-type function and if p? is accepted using p? as the resulting momentum p and starting position q as the resulting position q or if it is rejected, using p as the resulting momentum p and starting position q as the resulting position; and wherein the molecular dynamics step comprises: given a starting position q and starting momentum p of the molecular system, running a molecular dynamics simulation over a fixed number of iterations and obtaining new position q? and new momentum p?; evaluating the shadow