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Electrodermal activities (EDA) are any electrical phxenomena observed on the skin. Skin conductance (SC), a measure of EDA, shows fluctuations due to autonomic nervous system (ANS) activation induced sweat secretion. Since it can capture psychophysiological information, there is a significant rise in the research work for tracking mental and physiological health with EDA. However, the current state-of-the-art lacks a physiologically motivated approach for real-time inference of ANS activation from EDA. Therefore, firstly, we propose a comprehensive model for the SC dynamics. The proposed model is a 3D state-space representation of the direct secretion of sweat via pore opening and diffusion followed by corresponding evaporation and reabsorption. As the input to the model, we consider a sparse signal representing the ANS activation that causes the sweat glands to produce sweat. Secondly, we derive a scalable fixed-interval smoother-based sparse recovery approach utilizing the proposed comprehensive model to infer the ANS activation enabling edge computation. We incorporate a generalized-cross-validation to tune the sparsity level. Finally, we propose an Expectation-Maximization based deconvolution approach for learning the model parameters during the ANS activation inference. For evaluation, we utilize a dataset with 26 participants, and the results show that our comprehensive state-space model can successfully describe the SC variations with high scalability, showing the feasibility of real-time applications. Results validate that our physiology-motivated state-space model can comprehensively explain the EDA and outperforms all previous approaches. Our findings introduce a whole new perspective and have a broader impact on the standard practices of EDA analysis.