Submanifolds in the thermodynamic phase space (Q1081159)

Thermodynamic phase space (TPS) is a contact manifold \((M,\theta)\) of dimension \(2n+1\). Some constraints are often imposed on the thermodynamic processes. The paper proposes a method to find in TPS surfaces which represent admissible states of a given thermodynamic system and which are consistent with imposed constraints. This method consists of three steps: (1) to find a suitably defined reduced contact space with a reduced contact form \(\theta'\); (2) to find the Legendre submanifolds of the equation \(\theta'=0\); (3) to extend these submanifolds by singularity of form \(\theta\) restricted to the constraints.