By: Mário Pinheiro
From: Instituto Superior Técnico
At: Instituto de Investigação Interdisciplinar, Anfiteatro
This lecture deals with a new variational principle for out-of-equilibrium physical systems and how it can be useful to study nature under the scientific point of view.
The proposed method is fundamentally based on the method of Lagrange multipliers applied to the total entropy of an ensemble of particles. However, the theoretical innovation is the result of the philosophical assumption that in Nature the struggle of the opposed is crucial to surpass inertia (Hegel ditto). The most appropriate methodological approach for investigating along this path is to use the fundamental equation of thermodynamics on differential forms, considering the energy and the entropy as 0-forms. This approach gives us a set of two first order differential equations that reveal the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. Interestingly, it is found an unknown topological torsion current. Going deeper in this procedure, it is derived a special form of the Umov-Poynting theorem for rotating gravito-electromagnetic systems. The variational method is then applied to clarify the working mechanism of particular devices, in particular clarifying why plasma in a Tokamak or plasma arc can turn in retrograde or amperian rotation. The lesson we learned is that in Nature processes result from a balance between energy and entropy, with each attempting to achieve a different equilibrium condition.