Cohomology in algebra, geometry, physicsand statistics

Differential invariants in thermodynamics

It is well known that contact geometry gives the appropriate framework for formulating thermodynamics: Thermodynamic states can be interpreted as Legendrian submanifolds of a certain contact manifold. The existence of a metric on thermodynamic states has also received some attention in the last decades. The metric can be interpreted as the variance of an underlying probability measure. Less studied is the action of the affine group that appears naturally in this context as the group preserving the variance. We study this group action by finding generators of its algebra of scalar differential invariants, which intuitively can be thought of as the observables in the theory. In the end, we discuss the relation between the invariants and some well-known physical quantities in thermodynamics.

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We  shall  start    at 11.AM   at ZOOM,   Meeting ID: 895-276-2498 , for      virtual coffee before    the lecture.    A direct link     to    the  ZOOM meeting   shall be   sent  to you     at  10 AM     Wednesday   April 15.  After    the end  of seminar   we   still  have  30 minutes for     discussion.