The existence of a canonical tetra-stranded hereditary polymer requires more than structural plausibility: it must satisfy thermodynamic conditions that favor a genome-scale four-strand state over duplex or partially folded alternatives. In this work, I develop a minimal thermodynamic framework for Q-DNA, decomposing the free energy of a tetra-stranded genome into enthalpic interactions, electrostatic contributions, and entropic penalties associated with strand confinement and ordering. I derive stability thresholds as functions of temperature, ionic composition, and molecular crowding, and I predict the existence of environmental stability windows in which Q-DNA dominates the free-energy landscape. This framework provides quantitative criteria for canonicality and establishes testable predictions for experimental and synthetic realizations of tetra-stranded genomes. Keywords: Q-DNA, tetra-stranded genome, thermodynamics, free energy, entropy, electrostatics, molecular crowding