Research led by Manuel de Leónprofessor and researcher at the CSIC and member of the expert group of the Rafael del Pino Foundation Chair in Science and Societyproposes a novel way of describing thermodynamic systems, i.e. those involving the heat, energy and matter.
Normally, thermodynamics has been studied using contact geometry. As explained in the paper, entitled "A geometric description of some thermodynamical Systems". and published in Journal of Physics A: Mathematical and TheoreticalManuel de León and Jaime Bajoof the University of Valladolidhave used a special type of geometry based on what they call "(almost) cosymplectic structures".The new report, which suggests that it may become a natural extension, is a good example of this.
The symplectic structures make it possible to measure "areas" in higher-dimensional spaces, in a process similar to that used to measure two-dimensional areas in Euclidean geometry. By applying this new geometrical description, the authors manage to obtain the same evolution equations for these thermodynamic systems that had already been discovered by other scientists such as Gay-Balmaz and Yoshimura in 2019. This means that this new way of looking at things is valid and consistent with what was already known.
The main benefit of this new method is that it allows for the implementation of new geometric tools to study and solve complex problems in thermodynamics. For example, it can be used to understand how the systems change over time (evolution equations); to simplify the study of systems that have symmetriesi.e. properties that do not change, even if the system is transformed in certain ways; understanding the principle of Hamilton-Jacobiwhich is used to describe how systems evolve; and help to discretise These systems are useful for computer simulations.
The article applies this new description to several types of increasingly complex thermodynamic systems. In the case of simple systems adiabatically closedsystems do not exchange heat and matter with the outside world and have only one entropy variable; systems with internal mass transfer are those in which matter moves between different internal compartments; the systems in which matter moves between different internal compartments; the systems adiabatically closed non-simpleThe systems are more complex, incorporating several entropy variables and possible processes such as heat conduction; finally, the systems are more complex, incorporating several entropy variables and possible processes such as heat conduction. open can exchange heat and matter with the outside world.