  We investigate the thermodynamic constraints on the pivotal task of
entanglement generation using out-of-equilibrium states through a
model-independent framework with minimal assumptions. We establish a necessary
and sufficient condition for a thermal process to generate bipartite qubit
entanglement, starting from an initially separable state. Consequently, we
identify the set of system states that cannot be entangled, when no external
work is invested. In the regime of infinite temperature, we analytically
construct this set; while for finite temperature, we provide a simple criterion
to verify whether any given initial state is or is not entanglable.
Furthermore, we provide an explicit construction of the future thermal cone of
entanglement - the set of entangled states that a given separable state can
thermodynamically evolve to. We offer a detailed discussion on the properties
of this cone, focusing on the interplay between entanglement and its volumetric
properties. We conclude with several key remarks on the generation of
entanglement beyond two-qubit systems, and discuss its dynamics in the presence
of dissipation.
