Entropy and stability in a stochastic laser model

Junhua Chen, Hong-Yi Fan

Swarnav Banik, Elliot Greenwald, Xing Pan

Laser frequency stabilization is conventionally analyzed using continuous-time control theory, which accurately models analog feedback but is insufficient for digital implementations where quantization, sampling, and stochastic noise shape the dynamics. In modern digital laser systems, such as Photonic Integrated Circuit (PIC)-based lasers, finite discriminator and actuator resolution, sampling delays, and measurement noise introduce stochastic behavior that deterministic models do not capture. We present a discrete-time Markov-state framework that models the evolution of the quantized actuator in a digital laser frequency lock, with state-transition probabilities determined by the frequency discriminator response, noise statistics, and implemented digital control logic. The steady-state actuator and locked-laser frequency distributions are obtained directly from the unit-eigenvalue solution of the transition matrix, providing immediate access to key stability metrics without long time-domain simulations. For white frequency noise, we show that the Markov formulation is exact under decorrelated sampling and update schemes, while correlated discriminator sampling introduces a predictable inflation of actuator variance without shifting the operating point. In the presence of colored noise, long-range temporal correlations induce sampling-dependent deviations in both actuator mean and variance, defining the regime of validity of the memoryless Markov description. This framework provides a compact and physically transparent tool for analyzing and optimizing digitally stabilized lasers in integrated photonic systems.

Richard M. Sillitto

Nikos Demopoulos

The role of randomness in physical systems remains a pivotal topic, influencing the transition from quantum mechanics to classical stability and shaping complex dynamic behaviors. This paper explores the concept of stochastic determinism, illustrating how stochastic processes contribute to order in classical and quantum systems. By integrating stochastic differential equations (SDEs), entropy-driven self-organization, and fluctuation-dissipation principles, we demonstrate that randomness is not merely an obstacle to predictability but a key mechanism for structure formation. The study further examines applications in thermodynamics, turbulence, and quantum decoherence, bridging stochasticity and determinism as complementary aspects of physical reality.

M. Lax

Halil Özbil

The Poisonous Lattice Framework introduces an adaptive entropy-reactive security architecture in which adversarial access attempts trigger controlled informational collapse toward maximum-entropy states.Unlike classical cryptographic paradigms based solely on passive secrecy and computational hardness, the framework proposes active information neutralization: under intrusion conditions, the system dynamically degrades extractable informational structure through entropy injection and stochastic collapse dynamics.The framework combines:density operator theory,von Neumann entropy dynamics,Lindblad-type master equations,stochastic Lyapunov stability analysis,quantum information geometry,and adaptive post-quantum LWE-inspired degradation mechanisms.Theoretical results include:global asymptotic convergence toward the maximally mixed state,entropy monotonicity under adaptive collapse,stochastic stability guarantees,Holevo-bounded adversarial information extraction,and adaptive noise-coupled security degradation.This work is presented as a theoretical research framework and mathematical demonstrator for:adaptive cyber defense,anti-tamper architectures,intrusion-reactive information systems,post-quantum security concepts,and entropy-driven runtime protection mechanisms.The framework does not claim unconditional cryptographic security or production-ready implementation. Future work includes simulation validation, hardware-oriented architectures, runtime telemetry analysis, and experimental anti-extraction systems. �