An interesting class of physical systems, including those associated with life, demonstrates the ability to hold thermalization at bay and perpetuate states of high free-energy compared to a local environment. In this work we study quantum systems with no external sources or sinks for energy, heat, work, or entropy that allow for high free-energy subsystems to form and persist. We initialize systems of qubits in mixed, uncorrelated states and evolve them subject to a conservation law. We find that four qubits make up the minimal system for which these restricted dynamics and initial conditions allow an increase in extractable work for a subsystem. On landscapes of eight co-evolving qubits, interacting in randomly selected subsystems at each step, we demonstrate that restricted connectivity and an inhomogeneous distribution of initial temperatures both lead to landscapes with longer intervals of increasing extractable work for individual qubits. We demonstrate the role of correlations that develop on the landscape in enabling a positive change in extractable work.

Topologically Invariant!Topology is a branch of mathematics that concerns understanding 'shape' by studying the properties of objects (including many abstract ones) that are invariant under continuous transformations (modiſcations) like stretching or bending, but not tearing. Informally, topology is also referred to as rubber sheet geometry. Among the closed surfaces that we encounter, like the surface of a ball (sphere), surface of the doughnut (torus), or surface of a tray (or cup) with many handles, it turns out that those with the same number of holes are equivalent, while those with differing number of holes are not.