We present a complete thermodynamic analogy of statistical energy analysis (SEA) using entropy and energy for both linear and nonlinear coupled systems. We will use Khinchin’s Entropy as our statistical entropy definition from statistical mechanics. This framework allows for the restrictive assumptions of linearity to be removed from this analysis method. We will use the classical definition of entropy to relate entropy to Vibrational Temperature. Using Khinchin’s statistical definition of entropy for a vibrating system, we will define a Vibrational Temperature as a function of energy. Hence, we will derive all that is necessary to construct the SEA power flow equation along with the transient coupling loss factors without any linearity assumption. With this method one can expand SEA to nonlinear transient coupled systems. We will verify our proposed method using Monte Carlo Simulation and published analytical closed form solutions.