DFT protocols for quantum thermodynamics of out-of-equilibrium systems

Quantum thermodynamics strives to understand quantum fluctuations at the nanoscale, with an emphasis on the determination of thermodynamic properties of out-of-equilibrium quantum systems. This already challenging task becomes significantly more complex when many-body interactions give rise to strongly correlated systems. Inspired by the Kohn-Sham approach to Density Functional Theory (DFT), we propose to tackle this problem in a framework where the system is effectively described by non-interacting particles, and extend the protocol introduced in M. Herrera, R.M. Serra, I. D’Amico, Scientific Reports 7, 4655 (2017). Considering all dynamic regimes, from adiabatic to sudden quench, we study the work extraction and entropy production in finite Hubbard chains up to 8 sites, and compare results from various driving potentials. We examine the competition between the evolution time, interaction strength, and thermal regimes, benchmarking approximate results against the exact ones. Our results reveal that the DFT-inspired protocol performs well, with deviation of less than 10%, compared to the exact results up to moderate coupling regimes and, surprisingly for a ground state DFT protocol, up to intermediate temperatures of KT~2-3 J, J the hopping parameter.