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

• URL: http://arxiv.org/abs/2301.11548v4
• Date: Wed, 19 Feb 2025 13:17:42 GMT
• Title: No-Signaling in Steepest Entropy Ascent: A Nonlinear Non-local Non-equilibrium Quantum Dynamics of Composite Systems
• Authors: Rohit Kishan Ray, Gian Paolo Beretta,
• Abstract summary: Lindbladian formalism models open quantum systems using a 'bottom-up' approach, deriving linear dynamics from system-environment interactions. We present a 'top-down' approach, focusing on system's structure, subsystems' interactions, environmental effects. We show that incorporating the second law's requirement -- that Gibbs states are the sole stable equilibria -- necessitates nonlinear dynamics.
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• 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.

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