Black rings and the physical process version of the first law of thermodynamics

We consider the problem of the physical process version of the first law of black ring thermodynamics in $n$-dimensional Einstein gravity with additional $(p+1)$-form field strength and dilaton fields. The first order variations of mass, angular momentum and local charge for black ring are derived. From them we prove the physical process version of the first law of thermodynamic for stationary black rings.