# The first law of thermodynamics: a formalism

We provide a formalism for the first law of thermodynamics: an invariant quantity of an object on a sphere. We obtain a universal formula for the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker vacuum, which is invariant under the first law. We show that the equation of state equation for Minkowski vacuum is solved in the largest dimension, and the equation of state equation for Quark-gluon plasma is solved in the smallest dimension, and that the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker are the same as those of the thermodynamical quantities of Quark-gluon plasma. The latter were originally obtained in volume and mass formulas and have been generalized to multiple dimensions. We discuss the relation to the first law of thermodynamics and provide a formula for the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker. This formula is invariant under the first law of thermodynamics. We present the formula for the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker; it is invariant under the first law of thermodynamics.