Definition of a time variable with Entropy of a perfect fluid in   Canonical Quantum Gravity
  The Brown-Kuchar mechanism is applied in the case of General Relativity coupled with the Schutz model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy. 
Francesco Cianfrani (1), Giovanni Montani (1, 2 and 3), Simone Zonetti   (4) ((1) Dipartimento di Fisica, Universita degli S...