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.

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 simple 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 qubit systems in mixed, uncorrelated states and evolve them subject to a conservation law. We find that four qubits, one of which sets the reference temperature, make up the minimal system for which these restricted dynamics and initial conditions allow an increase in extractable work for a subsystem. We then consider landscapes of eight qubits where unitary, energy and excitation-number conserving evolution happens among neighbors randomly selected at each step. We study the frequency of time-steps with positive change in extractable work, and the total increase in extractable work. We show how the level of diversity in the initial state, the connectivity of the qubits, and the choice of unitary within the allowed family affect the frequency of instances where individual qubits experience an increase in extractable work.