  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.)
