Using the Coleman-Noll theories, we have developed a new description of the free energy change on deformation, Psi, including volume change and the time and temperature dependencies. Psi depends on three new principal invariants: sI_1, sI_2, and sI_3. These depend on the Hencky strains, ln lambda, instead of the stretch ratios lambda. Here, we test the applicability of the theory to the observed ... [Show full abstract] behavior of unfilled natural and styrene-butadiene elastomers under the assumption of incompressibility (where sI1 is a constant). We use literature data on isothermal, isochronal (or nearly so) response in large deformation, biaxial, planar sheet stretching in single step, step-up, stress relaxation. The two invariant functions partial Psi/partial sI2 and partial Psi/partial sI3 are calculated at constant sI2 and sI3 via the Valanis-Landel function, lambda w¢(lambda). Their dependencies on sIi at constant sIj are astonishingly simple and straightforward. Hence, over the conditions reported, Psi can now be completely defined analytically without a prior assumption about its invariant dependence.