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Physics-based first-principles pressure-volume-temperature equations of state(EOS) exist for solids and gases but not for liquids due to the long-standingfundamental problems involved in liquid theory. Current EOS models that areapplicable to liquids and supercritical fluids at liquid-like density underconditions relevant to planetary interiors and industrial processes are complexempirical models with many physically meaningless adjustable parameters. Here,we develop a generally applicable physics-based (GAP) EOS for liquids includingsupercritical fluids at liquid-like density. The GAP equation has only onedimensionless parameter: the Gr\"uneisen parameter for the fluid. The GAPequation is explicit in the internal energy, and hence links the mostfundamental macroscopic static property of fluids, thepressure-volume-temperature EOS, to their key microscopic property: themolecular hopping frequency or liquid relaxation time, from which the internalenergy can be obtained. We test our GAP equation against available experimentaldata in several different ways and find good agreement. We observe that the GAPequation is similar to the Mie-Gr\"{u}neisen solid EOS in a wide range of theliquid phase diagram. This similarity is ultimately related to the condensedstate of these two phases. On the other hand, the differences between the GAPequation and EOS for gases are fundamental. Finally, we identify the key gapsin the experimental data that need to be filled in to proceed further with theliquid EOS.

Generally applicable physics-based equation of state for liquids