The EXP pair-potential system. IV. Isotherms, isochores, and isomorphs in the two crystalline phases

Extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures

This paper studies numerically the Weeks-Chandler-Andersen system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures.

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

Isomorph theory beyond thermal equilibrium

This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(R_a) < U(R_b) ⇒ U(λR_a) < U(λR_b). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.