I have information about temperature, pressure, normal and shear stresses, viscosity, conductivity, density, heat capacity and adiabatic heating for a particular area of mantle in the form of 2D matrices. I want to show phase relation for this region of mantle. Is there an equation (group of equations) which relates phase relation for mantle with these properties?
Perple_X (http://www.perplex.ethz.ch/) is software designed to do exactly that.
It has thermodynamic and mineral property databases for phases in interest. This is pretty much automation of method 3 given by the other answer.
In short, the way it works: you input your bulk composition, pressure, and temperature, and it spits out the phase relations.
A bit of warning: this software is very poorly documented with many tutorials and guides referring to older version that don't work exactly like the new one. I recommend going on their discussion forum which is very active, and the developer himself is commonly there. He is usually very responsive and can fix bugs pretty much on the spot (time-zone constraints permitting).
There are a couple of ways of going about this, but all require you to know the bulk composition of the system (usually given in wt% oxides).
Once you have that you can...
1) use a program like MELTS to calculate the phase equilibria.
2) Do some type of normative mineralogy calculation (see, for example, the CIPW norm). These sorts of heuristics depend on the P,T conditions.
3) Bust out your knowledge of thermodynamics and calculate the change in Gibbs Free Energy for the permutations of all the possible phases. I don't recommend doing this - it will take a very long time.