1307.7512 (Antonio Moro)

Shock dynamics of phase diagrams    [PDF]

Antonio Moro

We propose a novel description of phase diagrams of van der Waals type fluids based on the semiclassical theory of viscous shock waves. We develop the approach to classical thermodynamics recently introduced in [6] by considering a generalised family of nonlocal entropy functions. Such nonlocal entropies lead to the formulation of the first law of thermodynamics in terms of a nonlinear viscous conservation law. This theory provides an analytic description of discontinuities of the order parameter within the phase transition region where the classical van der Waals theory departs from the observed physical behaviour. We show that near the critical point, in a suitable multisclale limit, all equations of state are obtained as solutions to the Burgers equation and as a consequence of a classical result due to Il'in they have one and the same universal form. Interestingly, the Burgers dynamics provides also a natural interpretation of triple points in terms of the shock confluence phenomenon in viscous systems.

View original: http://arxiv.org/abs/1307.7512