  Fluid polyamorphism, the existence of multiple amorphous fluid states in a
single-component system, has been observed or predicted in a variety of
substances. A remarkable example of this phenomenon is the fluid-fluid phase
transition in high-pressure hydrogen between insulating and conducting
high-density fluids. This transition is induced by the reversible
dimerization/dissociation of the molecular and atomistic states of hydrogen. In
this work, we present the first attempt to thermodynamically model the
fluid-fluid phase transition in hydrogen at extreme conditions. Our predictions
for the phase coexistence and the reaction equilibrium of the two alternative
forms of fluid hydrogen are based on experimental data and supported by the
results of simulations. {Remarkably, we find that the law of corresponding
states can be utilized to construct a unified equation of state combining the
available computational results for different models of hydrogen and the
experimental data.
