In this manuscript we present the thermodynamics of iron-carbon nano particles at low temperature. By combining classical molecular dynamics simulations, ab initio calculations, finite temperature thermodynamics modeling, and the “size/pressure approximation”, we address carbon-induced fluidization, size-induced eutectic point shift, and reduced solubility at the nanoscale. The results are used to describe, as functions of particle size, three scenarios in the catalytic chemical vapor deposition growth of single single-walled carbon nanotubes, corresponding to steady state-, limitedand no-growth.