Positive paths in diffeomorphism groups of manifolds with a contact distribution

Abstract Given a cooriented contact manifold , it is possible to define a notion of positivity on the group of diffeomorphisms of , by looking at paths of diffeomorphisms that are positively transverse to the contact distribution . We show that, in contrast to the analogous notion usually considered on the group of diffeomorphisms preserving , positivity on is completely flexible. In particular, we show that for the standard contact structure on any two diffeomorphisms are connected by a positive path. This result generalizes to compactly supported diffeomorphisms on a large class of contact manifolds. As an application, we answer a question about Legendrians in thermodynamic phase space posed by Entov, Polterovich, and Ryzhik in the context of thermodynamic processes.