The purpose of this paper is to investigate the construction of a statistical approach as a heuristic tool to understand the relations between mechanics and thermodynamics inside Ludwig Boltzmann's (1844-1906) research program. In this context, J.C Maxwell's (1831-79) distribution function of molecular velocities, which Boltzmann interpreted in different ways, will have a central role for being the source of new heuristic tools, such as the ''statistical ensemble" and the ''probability of state". These represent a conceptual effort as they associate the probability of its realization to the state of the phenomenon under analysis.
statistical mechanics; Ludwig Boltzmann; heuristics
