Increasing free-energy gain on co-evolving qubit networks

An interesting class of physical systems, including those associated with life, can hold thermalization at bay and perpetuate states of high free energy compared to a local environment. The subsystems evolve in a way that depends on and restricts the dynamics of the neighboring subsystems and the environment. How does the network of interactions between subsystems assist in perpetuating states of high free energy?

We study a closed, co-evolving network of twelve qubits with no external sources or sinks for energy, heat, or work that allows for high free-energy subsystems to form and persist. Sets of subsystems are randomly selected and undergo simultaneous evolution. We find that a restricted network and an inhomogeneous distribution of initial states lead to subsystems with longer intervals of high free energy. Additionally, we find that subsystems in the same environment with and without subsystem-environment correlation lead to different thermodynamic outcomes. We derive the phase-covariant dynamical maps that describe the evolution of subsystems and present bounds on the map parameters given by the information flow on the qubit network. To conclude, we present a class of dynamical maps that induce persistent high free energy states of the subsystem.