Information Backflow Diagrams Unify Entanglement Revivals and Entropy Overshoots in Models

Why It Matters

The NI functional offers a universal, quantitative tool to classify non‑Markovian behavior, enabling cross‑disciplinary comparison and guiding the design of systems where memory control is critical.

Key Takeaways

• NI functional integrates positive information flow intervals.
• Fractional exponent α≈0.5 marks non‑Markovian transition.
• Quantum revivals and entropy overshoots share backflow.
• Models use Mittag‑Leffler kernel for long‑tailed memory.
• Framework is model‑agnostic, applicable to broader systems.

Pulse Analysis

Non‑Markovian dynamics, where a system’s future depends on its past, have long been diagnosed separately through quantum entanglement revivals or classical entropy overshoots. The new backflow diagram consolidates these signatures by focusing on the direction of information flow rather than the specific observable. By integrating only the positive increments of an information‑like quantity, the NI functional captures the essence of memory return, offering a clear, quantitative boundary between Markovian decay and genuine backflow. This shift from symptom‑based detection to a unified metric simplifies comparative studies across disparate physical platforms.

On the quantum side, the authors extend a two‑state relaxation model with a Caputo fractional derivative, yielding a Mittag‑Leffler decay that decays slowly and supports repeated entanglement revivals. The analytic expression for the intrinsic entanglement component shows that the revival amplitude is directly tied to the fractional order α, with a critical value near 0.5 separating monotonic loss from oscillatory resurgence. Embedding the system in a thermo‑field dynamics framework makes hidden auxiliary modes explicit, demonstrating that the backflow originates from the memory kernel’s structure rather than external parameters.

The classical counterpart employs a three‑state semi‑Markov process with Erlang‑2 waiting times, mirroring the quantum findings through entropy overshoots and KL‑divergence spikes. Introducing the same Mittag‑Leffler kernel reproduces the α≈0.5 transition, confirming that the kernel’s mathematical form governs non‑Markovianity across both realms. This universality opens pathways to apply the NI functional to more complex quantum devices, biochemical networks, and engineered reservoirs, where controlling memory effects can enhance performance, stability, or information processing capabilities.