Uso de la tecnología para facilitar la comprensión del teorema de liouville de la física estadística, en estudiantes de licenciatura en física de la Universidad Distrital Francisco José de Caldas

Abstract

In the present work, the goal is to establish an understanding of Liouville's Theorem through a mixed-method approach (qualitative and quantitative) with two groups of ninth-semester students in the Physics Bachelor's program at the UD, in the Statistical Physics course. The issue of phase volume conservation, central to Liouville's Theorem, is addressed with two didactic sequences: one experimental, using fluid dynamics with ideal flow, and another through a software tool with a prototype in Processing. The experimental group constructs an artifact to generate an ideal water flow and studies the change in the area of floaters before and after a change in cross-sectional area. The software group adapts the provided code and conducts a similar study of the area change of points that flow before and after the change in cross-sectional area. Upon completion of the work, each group is interviewed separately, using a table of categories and subcategories for qualitative classification with the QDA Miner Lite software. Subsequently, a quantitative analysis is carried out to assign a statistical weight to the categories and subcategories. The results indicate that the dominant forms of approach are mathematical and ascending abstraction, with a combined weight of approximately 60%. This suggests that students recognize mathematics not only as a tool but also as a language that describes the ontological reality of the physical world. However, due to the complexity of Liouville's Theorem in a hyper-dimensional phase space, students use analogies from the experimental and computational didactic sequences to establish cognitive links that facilitate their understanding using ascending abstraction.