Entropy, Information, Chaos and the Quantum Potential

Jincheng Zhang

This paper investigates the potential of quantum chaotic systems to store information entropy. We propose a framework leveraging the inherent complexity of chaotic states in quantum systems to facilitate information storage. The core concept involves mapping the dynamics of a quantum chaotic system to represent and preserve information, drawing parallels between the storage capacity of chaos and the concept of entropy. We explore theoretical formulations of this approach, focusing on the relationship between the system's parameters, the generated chaotic behavior, and the resulting information storage capacity. Our work aims to contribute to the burgeoning field of quantum information storage and potentially illuminate the fundamental connection between chaos and information processing. The methodology presented allows for a novel approach to information storage using quantum phenomena, offering a theoretical foundation for future research and development. The core claim is the utilization of quantum chaotic states to achieve information entropy storage, while the core mechanism involves combining the complexity of chaotic states with the storage capabilities of entropy. ---

Subhash C. Kak

Nilanjana Datta

Jincheng Zhang

This paper explores the intersection of information theory and quantum chaos, proposing a novel framework to understand the evolution and resonance of chaotic systems. We introduce a quantum chaos model based on information entropy, demonstrating how this approach can predict and potentially control the behavior of quantum systems. The core claim is that information plays a fundamental role in the emergence of chaos in quantum systems, and that analyzing information-theoretic properties can guide the design of robust quantum algorithms. This work moves beyond traditional chaos theory by incorporating information principles, offering a new perspective on the dynamics of quantum phenomena. We detail the model's mathematical foundation, explain the connection between information entropy and the emergence of chaos, and present preliminary results demonstrating the model's predictive capabilities. The paper concludes with a discussion of the implications for quantum computing and information processing.

Robert Sims, Daniel Ueltschi

Tara Bahadur Rana, Yadav Raj Dahal, Kiran Adhikari

In this work, we study pseudo entropy and spectral dynamics in quantum spin chains (Heisenberg XXZ model and the mixed-field Ising model) to investigate whether they can serve as diagnostics of quantum chaos. First, we derive an exact relation between the real part of the thermal pseudo entropy and the spectral form factor. This provided evidence that pseudo entropy could exhibit the characteristic dip, logarithmic ramp, and plateau, implying the precise manner in which pseudo entropy probes chaos. We found that the imaginary part, while it does not diagnose chaos, can still provide crucial information about Fisher zeros that is not available in the real counterpart. For spatial pseudo entropy in the XXZ chain, we find that the logarithmic critical scaling persists in both integrable and chaotic regimes, and that the non-positivity conjecture holds. Finally, we derive an exact connection between pseudo entropy, relative pseudo entropy, and spectral complexity with a potential connection to holography.