In the course of this research project, our initial step involves the generation of samples within the microcanonical set employing the Gradient Descent approach. Subsequently, we delve into a comprehensive examination of our proposed methodology, specifically focusing on its efficacy in estimating the entropy associated with the samples derived from this mode. This multi-faceted investigation encompasses a thorough exploration of the intricacies involved in the application of Gradient Descent for sample generation within the microcanonical set, followed by a detailed analysis of the entropy estimation process applied to the resultant samples. The extended exploration of these key aspects aims to provide a nuanced understanding of the capabilities and limitations of the proposed approach in the context of entropy estimation within the described modeling framework.