Deterministic generation of the Boltzmann–Gibbs distribution and the free energy calculation from the Tsallis distribution

A method for constructing the Boltzmann–Gibbs distributions is presented by combining the re-weighting technique and the deterministic dynamical equation that produces the Tsallis distributions. The ability to produce the Boltzmann–Gibbs distributions is shown by calculating the distribution, the energy with higher moments, and the Helmholtz free energy. From numerical simulations of a small system that represents a fundamental chemical interaction model, correct answers were obtained within a wide range of temperatures. An application to a peptide system is also shown.