  A thermodynamic phase transition denotes a drastic change of state of a
physical system due to a continuous change of thermodynamic variables, as for
instance pressure and temperature. The classical van der Waals equation of
state is the simplest model that predicts the occurrence of a critical point
associated with the gas-liquid phase transition. Nevertheless, below the
critical temperature, theoretical predictions of the van der Waals theory
significantly depart from the observed physical behaviour. We develop a novel
approach to classical thermodynamics based on the solution of Maxwell relations
for a generalised family of nonlocal entropy functions. This theory provides an
exact mathematical description of discontinuities of the order parameter within
the phase transition region, it explains the universal form of the equations of
state and the occurrence of triple points in terms of the dynamics of nonlinear
shock wave fronts.
