Quantifying Behavioral Entropy as a Mechanistic Indicator of Neural State Under Sleep Deprivation in Drosophila melanogaster

In the United States, coffee is the most widely consumed beverage, with approximately 68% of Americans drinking it daily (National Coffee Association, 2025). Caffeine is widely used as a neural stimulant (Rehm et al., 2020); however, its consumption has been associated with negative health effects including cardiovascular issues, insomnia, anxiety, and reduced bone density in women (Bordeaux, 2025; Cizmarova et al., 2025). These concerns motivate the search for alternative dietary compounds capable of sustaining cognitive alertness while minimizing system instability. From a statistical physics standpoint, such compounds may act as external agitators capable of shifting the stability of biological systems away from equilibrium. This study investigates locomotor dynamics in sleep-deprived Drosophila melanogaster as a model system to evaluate the effects of caffeine and plant-derived polyphenols on neurobehavioral system stability. Drosophila were subjected to chronic sleep deprivation and randomly assigned to one of nine dietary treatment groups containing varying concentrations of caffeine, polyphenols, or a combination of both. Furthermore, two-dimensional motion trajectories were recorded and analyzed as stochastic processes that evolve in phase space. Entropy, Mean Squared Displacement (MSD), Diffusion Coefficient (D), Anomalous Diffusion (ɑ), and Drift were calculated to quantity individual and system-wide Drosophila behavior. Then, statistical analyses were performed using Kruskal-Wallis tests with a P value of p < 0.05. Results indicate that polyphenol-treated Drosophila exhibited the reduced behavioral entropy (H ≈ 0.62–0.68) as well as lower diffusion coefficients (D ≈ 0.48–0.54), indicating more stable system dynamics and decreased behavioral variability. In contrast, caffeine treatments increased both entropy and diffusion (H ≈ 0.72–0.81; D ≈ 0.60–0.71), with higher values for higher dosages of caffeine, reflecting increased system movement stochasticity. Control Drosophila displayed intermediate values (H ≈ 0.69; D ≈ 0.55) and provided a baseline for metric comparison. Overall, these findings show that polyphenols stabilize behavioral dynamics during sleep deprivation while caffeine amplifies system stochasticity. In a wider context, this work connects traditional statistical locomotion physics to neural states, creating a framework for describing macroscopic behavioral dynamics in sophisticated biological systems.