No-Signaling in Steepest Entropy Ascent: A Nonlinear Non-local Non-equilibrium Quantum Dynamics of Composite Systems

TL;DR

This paper develops a nonlinear, non-local quantum dynamics framework based on a top-down variational principle, ensuring thermodynamic consistency and no-signaling in composite systems, advancing the integration of quantum mechanics and thermodynamics.

Contribution

It introduces a top-down approach using steepest-entropy-ascent principles to model non-equilibrium quantum dynamics that preserve no-signaling in composite systems.

Findings

Reintroduction of local perception operators enables signaling-free non-local effects.

Demonstration of the steepest-entropy-ascent variational principle's validity in quantum thermodynamics.

Potential applications in quantum computing and resource theories.

Abstract

The 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 system's structure, subsystems' interactions, 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.