We propose to organize a school in 2016 on the thermodynamical modeling of natural silicate liquids and their associated fluids using the MELTS software package (Ghiorso and Sack, 1995; Asimow and Ghiorso, 1998). MELTS is a software package designed to facilitate thermodynamic modeling of phase equilibria in magmatic systems. Revised calibrations of the liquid thermodynamic model are available in pMELTS (Ghiorso, Hirschmann, Reiners and Kress, 2002). (p)MELTS is based on a database of experimental results up to 2000 °C and 3 GPa.
Then we present a series of complementary lectures and practical tutorials on first-principles molecular dynamics (FPMD). In MD the atoms move according to Newtonian dynamics under the action of interatomic forces. In FPMD the ionic forces are computed directly from the electronic structure of the system, which is obtained by solving an approximate form of the Schrödinger equation. We will present different ensembles, statistical analysis of the MD runs, and applications in geophysics; we will discuss path integral molecular dynamics. We will complement the theoretical part with two lectures on experimental apparatus and in situ measurements.

MELTS:
- Evolution scenarios for magmatic processes modeled as a series of steps in temperature and pressure (Gibbs energy minimization), temperature and volume (Helmholtz energy minimization), enthalpy and pressure (entropy maximization) or entropy and pressure (enthalpy minimization).
- Isenthalpic (constant enthalpy), isentropic (constant entropy) or isochoric (constant volume) scenarios utilized to explore magmatic processes: energy constrained assimilation, adiabatic decompression melting, or post-entrapment crystallization in phenocryst melt inclusions.
- Equilibrium computed in systems open to oxygen transfer at fixed chemical potential (fugacity) of oxygen.
- Equilibrium and fractional crystallization of magmas modeled along a specified oxygen buffer.

FPMD:
- Introduction in density-functional theory based first-principles molecular dynamics
- Presentation of different ensembles: isocanonical, isokinetical, isoenergetic, etc.
- Statistical analysis of the results: thermalization vs production runs, pair distribution functions, structure factor
- Transport properties: diffusion, viscosity
- Thermodynamic integration, melting curves, crystallization.

Experiments:
- Technics for in situ measurements in static presses: piston-cylinder apparatus, multi-anvil presses, diamond anvil cells
- Shock induced melting, melting curves, in situ measurements of transport properties.