  We build a comprehensive methodology for the fast computation of entropy
across both solid and liquid phases. The proposed method utilizes a single
trajectory of molecular dynamics (MD) to facilitate the calculation of entropy,
which is composed of three components. The electronic entropy is determined
through the temporal average acquired from density functional theory (DFT) MD
simulations. The vibrational entropy, typically the predominant contributor to
the total entropy, even within the liquid state, is evaluated by computing the
phonon density of states via the velocity auto-correlation function. The most
arduous component to quantify, the configurational entropy, is assessed by
probability analysis of the local structural arrangement and atomic
distribution. We illustrate, through a variety of examples, that this method is
both a versatile and valid technique for characterizing the thermodynamic
states of both solids and liquids. Furthermore, this method is employed to
expedite the calculation of melting temperatures, demonstrating its practical
utility in computational thermodynamics.
