Explorando a termodinâmica: desenvolvimento e programação de recursos didáticos virtuais

Abstract

Epistemological analysis is a research approach that investigates the origin and acquisition of knowledge. This study applies Imre Lakatos's Methodology of Scientific Research Programmes (MSRP) to analyze two bodies of thought: the laws of thermodynamics, i.e., conservation of energy, heat as a form of energy, and entropy increase for irreversible processes; and the classical Traveling Salesman Problem (TSP), evaluating competing theories that seek heuristic or exact combinatorial optimization methods. The analysis is supported by the perspective that mathematical modeling provides tools that facilitate the understanding, analysis, and solution of complex problems, especially in physics and computation. In the first case, thermodynamic cycles were modeled using the functional behavior of the isothermal, adiabatic, isobaric and/or isometric processes involved. In the context of the TSP, modeling can be done in terms of graphs, in which the vertices of the structure represent the cities that the salesman needs to visit and the edges indicate the connections between them. Applying the concurrent approach of the k­nearest neighbors algorithm, the distance between cities is calculated by the Euclidean distance between the points distributed in a network. Determining the value of k, representing the number of nearest neighbors, depends on the size of the data set, the complexity of the problem and the desired accuracy. Tracing the route to a new city involves calculating the distances to all the cities in the training set and identifying the k­nearest neighbors. The process must consider previously defined rules, such as not passing each point more than once and returning to the starting point. The primary output of these studies is a website hosted on Github of the homonymous book "From Micro to Macro: An Introduction to Thermostatistics". It is a free collaborative environment under construction, with user­friendly design providing static and dynamic content. The environment allows virtual evaluation tools to be embedded, which generate a database for validation by users and by a panel of experts. Key-words: Imre Lakatos, Research Program, Thermodynamics Cycles, Traveling Salesman Problem, mathematical modelling, Digital Information and Communication Technologies (DICT)