Grand Projection State: Bridge between Thermodynamic Variables and Spatial Constraint

Koretaka Yuge

Published 2016-04-20Version 1

In classical systems, we reexamine the relationship between thermodynamic variables (especially, focusing on grand potential and free energy) and spatial constraint on the constituents. We find that for R-component system, free energy in equilibrium disordered states can be well-characterized by 2(R-1) special microscopic states, which we call "grand projection states" (GP states). While the free energy depends on interactions, chemical potential and temperature, the GP states depend only on the class of spatial constraint, and are independent of interactions, chemical potential and temperature. The present findings therefore provides analytic determination of free energy as well as of mu-x relationship (mu: chemical potential, x: composition) from information about GP states, leading to significantly efficient prediction of phase boundary for disordered states or composition in subsystems equilibrated to thermal bath (e.g., surface or interface segregation).