Global cold curve. New representation for zero-temperature isotherm in whole density range

Non-standard representation for so-called "cold curve" of matter (i.e. isotherm $T = 0$) is proposed as Global Cold Curve (GCC). The main point is that chemical potential of substance, $\mu$, plays role of ruling parameter in basic GCC-dependence of internal energy under compression, $U = U(\mu)$, in contrast to the standard form $U = U(\rho)$. This substitution changes radically low-density ("gaseous") part of GCC. Namely: ($i$) - physically meaningless part of standard cold curve $(U(\rho)$ at $T \rightarrow 0)$ disappears totally from new version of GCC. This deleted part corresponded to absolutely thermodynamically unstable states in standard representation $U(\rho)$; ($ii$) - new gaseous branch of cold curve, $U = U(\mu)$, comes in GCC. It describes in simple, schematic way thermodynamics of whole gas-like plasma in low-temperature limit (Iosilevskiy: arXiv:0902.3708) as combination of all ionization and dissociation processes available for equilibrium plasma at finite temperature. This gaseous branch corresponds to thermodynamically stable and metastable states only. The only quantities that display themselves as meaningful details of new gaseous zero-temperature isotherm are combination of binding energies for all complexes (atomic, molecular and ionic) in their ground states, together with sublimation energy of gas-crystal phase transition ("energy scale" of material). Gaseous branch of GCC conjugate naturally with corresponding branch (cold curve) of condensed phase. New GCC form, $U = U(\mu)$, no more contains meaningless part of traditional form $U(\rho)$ between gaseous and crystalline spinodals. The simple schematic structure ("ionization stairs"), which is typical for new form of cold curve in ultra-low densities, appears again as "composition stairs" in ultra-high densities in typical conditions of interiors in compact stars (P.Haensel et al.)