Sub-system statistics for out-of-equilibrium qubits

Motivated by the thermodynamic evolution of both the homogeneous and inhomogeneous universe, we examine mini-landscapes of qubit systems initialized in inhomogeneous thermal states and evolved with dynamics constrained only by a conservation law. We establish the smallest closed-system size, four qubits, needed to model an increase in extractable work in sub-systems. We then consider larger closed-system qubit landscapes where interactions occur in four-qubit sets and study the evolution of the entropy, concurrence, and non-equilibrium free energy of sub-systems as a function of the inhomogeneity of the initial state. We present requirements, as a function of total system size, for pockets of low entropy and high free energy to persist.