  A liquid is termed strongly correlating if its virial and potential energy
thermal equilibrium fluctuations in the NVT ensemble are more than 90%
correlated [Phys. Rev. Lett. 100, 015701 (2008)]. The fluctuations of a
strongly correlating liquid are well approximated by those of an inverse
power-law intermolecular potential. Building on this fact we here define
"isomorphic lines" in the state diagram of a strongly correlating liquid. It is
shown from computer simulations of the Kob-Andersen binary Lennard-Jones liquid
that no aging is associated with jumps between two isomorphic points.
Isomorphic state points have the same excess entropy, the same reduced average
relaxation time, the same (reduced) dynamics, and the same scaled radial
distribution functions. Finally we calculate the equation for isomorphs in the
virial / potential energy diagram for Lennard-Jones type liquids and show that
all such 12-6 liquids have the same isomorphs; these may be scaled into a
master isomorph.
