Absolute equilibrium entropy

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magnetofluid turbulence is discussed, and the three-dimensional fluid case is examined in detail. A σ function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions σ and phase functions H (associated with the development of various H theorems of ideal turbulence). It is shown that the two approaches are complementary, though conceptually different: H theorems show that an isolated system tends to equilibrium, while σ functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.