Abstract
In this work, we consider the value of the momentum map of the symplectic mechanics as an affine tensor called momentum tensor. From this point of view, we analyze the underlying geometric structure of the theories of Lie group statistical mechanics and relativistic thermodynamics of continua, formulated by Souriau independently of each other. We bridge the gap between them in the classical Galilean context. These geometric structures of the thermodynamics are rich and we think they might be a source of inspiration for the geometric theory of information based on the concept of entropy.
Highlights
In [1], Souriau proposes to revisit mechanics, emphasizing its affine nature
Our starting point is closely related to Souriau’s approach on the basis of two key ideas: a new definition of momenta and the crucial part played by the affine group of Rn. This group proposes an intentionally poor geometrical structure. This choice is guided by the fact that it contains both Galileo and Poincaré groups [3,4], which allows the simultaneous involvement of the Galilean and relativistic mechanics
In order to discover the underlined geometric structure of the statistical mechanics, we are interested in the affine maps Θ on the affine space of momentum tensors
Summary
In [1], Souriau proposes to revisit mechanics, emphasizing its affine nature It is this viewpoint that we will adopt here, starting from a generalization of the concept of momentum under the form of an affine object [2]. A fruitful standpoint consists of considering the class of the affine tensors, corresponding to the affine group [2,5] This viewpoint is closely related to symplectic mechanics [3,4,6] in the sense that the values of the momentum map are just the components of the momentum tensors.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
