| Force-biased Monte Carlo (fbMC) methods have a long standing history as partners of Molecular Dynamics (MD) to simulate the evolution of materials at the atomic scale. Among these techniques, the uniform-acceptance force-bias Monte Carlo (UFMC) method, has recently attracted attention thanks to its apparent capacity of being able to simulate physical processes in a reduced number of iterations compared to classical MD methods. The origin of this efficiency remains however unclear. Through this work, we have derived a new UFMC method starting from basic thermodynamic principles which leads to an intuitive and unambiguous formalism. The approach has been extended to include a statistically relevant time-step per Monte Carlo iterations, showing a signicant speed-up compared to MD simulations. This formalism has been tested on both simple one-dimensional and more complex three dimensional systems. Both test-cases gave excellent results in agreement with analytical solutions and literature reports. The inclusion of a time-scale, the appealing simplicity of the method and the enhancement of the time-step compared to classical MD methods, make this method very appealing to study the dynamics of many-particles systems. |
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