where "t" = temperature, "s" = entropy, "p" = pressure, "v" = volume. the helmholtz free energy is often denoted by the symbol "f", but the use of "a" is preferred by iupac (see alberty, 2001). formula_1 is the number of particles of type "i" in the system. for the sake of completeness, the set of all formula_1 are also included as natural variables, although they are sometimes ignored.