No-Signaling in Steepest Entropy Ascent: A Nonlinear, Non-Local, Non-Equilibrium Quantum Dynamics of Composite Systems Strongly Compatible with the Second Law

Lindbladian formalism models open quantum systems using a 'bottom-up' approach, deriving linear dynamics from system-environment interactions. We present a 'top-down' approach starting with phenomenological constraints, focusing on a system's structure, subsystems' interactions, and environmental effects and often using a non-equilibrium variational principle designed to enforce strict thermodynamic consistency. However, incorporating the second law's requirement-that Gibbs states are the sole stable equilibria-necessitates nonlinear dynamics, challenging no-signaling principles in composite systems. We reintroduce 'local perception operators' and show that they allow to model signaling-free non-local effects. Using the steepest-entropy-ascent variational principle as an example, we demonstrate the validity of the 'top-down' approach for integrating quantum mechanics and thermodynamics in phenomenological models, with potential applications in quantum computing and resource theories.