  This paper tests how effectively the bound states of strongly interacting
gauge theories are amenable to an emergent description as a thermal ensemble.
This description can be derived from a conjectured minimum free energy
principle, with the entanglement entropy of two-parton subsystems playing the
role of thermodynamic entropy. This allows us to calculate the ground state
hadron spectrum and wavefunction over a wide range of parton masses without
solving the Schr\"{o}dinger equation. We carry out this analysis for certain
illustrative models in 1+1 dimensions and discuss prospects for higher
dimensions.
