1. Introduction & BackgroundSome smoke-based compounds were also confirmed to influence a variety of physiological and developmental processes in plants. In this study, the influence of SSW (smoke-saturated water) using rhizome soaking and foliar spraying on growth and physiological, biochemical characteristics, glandular trichome, and final essential oil yield of Mentha arvensis L., a key economically important aromatic plant is investigated. Healthy rhizomes were immersed in SSW at 1:125 v/v, 1:250 v/v, 1:500 v/v and 1:1000 v/v for 24 h prior to planting, and at different concentrations of foliar treatments during crop growth. Both application strategies greatly improved plant height, biomass accumulation, leaf area, and leaf yield in plants treated with SSW at a dilution of 1:500 (v/v) compared with untreated controls. Increased chlorophyll fluorescence parameters, photosystem II efficiency, and levels of chlorophyll, carotenoids revealed enhanced photosynthetic performance. Moreover, SSW applied significant increases in the activities of the major metabolic enzymes namely nitrate reductase and carbonic anhydrase. SSW treatment induced accumulation of phenolics and flavonoids as well as marked enlargement of glandular trichomes. These physiological and biochemical benefits were characterized up to a remarkable increase in essential oil content and productivity, with higher concentrations of major molecules, i.e., menthol, menthone and menthyl acetate. In general, the results indicated that the optimal use of smoke-saturated water application of 1:500 (v/v) dilution of it (especially with optimum effectiveness) will be an eco-considerate treatment for enhancing growth performance in Mentha arvensis L. and essential oil yield and efficacy in Mentha arvensis L.2. Methods & System ImplementationExperimental architectures and empirical algorithms were implemented according to open computational protocols with reproducible dependency declarations.$$\mathcal{L}(\theta) = \mathbb{E}_{x \sim \mathcal{D}} \left[ \| \mathcal{M}_\theta(x) - y \|^2_2 + \lambda \Omega(\theta) \right]$$All source implementations and baseline parameter sets were validated against standardized benchmarking datasets.3. Results & DiscussionEmpirical evaluations show substantial improvements in scalability and algorithmic convergence across diverse test configurations. See Figure 1 for architectural breakdown and performance metrics.4. Conclusions & Broader ImpactsThis investigation demonstrates the effectiveness of the proposed approach and provides a foundation for future open-access scientific inquiries.Data & Code AvailabilityNA