Calculation of the Production Function through Entropy: A Model from Econophysics

From an economic perspective, the problems associated with production require a model for its estimation. These estimations are typically made using the Cobb-Douglas production function, which is derived from least-squares adjustment. However, several authors have proposed alternative methods for calculating production based on the relationship between economic and thermodynamic problems. Our study provides a method for calculating the production function through entropy, which explicitly considers the contributions of labor and capital. In this way, we apply the model to the data presented in the Cobb-Douglas study on the production of the manufacturing sector in the United States. Our results accurately describe the production data, highlight the need to estimate the Boltzmann constant in the economic model, and provide a method for determining its value.