Foundations of molecular dynamics simulations: how and what

In this review, we discuss computational methods to study condensed matter systems and processes occurring in this phase. We begin by laying down the theoretical frame- work of statistical mechanics starting from the fundamental laws governing nuclei and electrons. Among others, we present the connection between thermodynamics and sta- tistical mechanics using a pure statistical language, which makes it easier to extend the microscopic interpretation of thermodynamic potentials to other relevant quanti- ties, such as the Landau free energy (also known as the potential of the mean force). Computational methods for estimating the relevant quantities of equilibrium and non- equilibrium statistical mechanics systems, as well as reactive events, are discussed. An extended Appendix is added, where we present artificial intelligence methods recently introduced. These methods can enhance the power of atomistic simulations, allowing to achieve at the same time accuracy and efficiency in the calculation of the quantities of interest.