A general approach is developed to individual analytic prediction of an energy state indexes for thermodynamic systems (TS) working under the nonequilibrium service conditions that cause determined and random degradation of the TS structures and performance: losses nominal levels of structure components and service properties characteristics. The following TS were proposed to be considered as relevant ones for the analysis: heat-resistant alloys; technology processes; climate, ecology and biology systems. Based on the energy conservation law, analytic relations were obtained for the TS service parameters calculations to specify conditions for the TS maximum performance reaching based on the TS individual structure features and a random factor values. The values have to be used in the relations may be rigorously experimentally or theoretically specified for each TS. The approach developed in the work was applied to predict creep temperature interval for industrial, austenite, particle hardened ASTM A316 steel. The basic possible strengthening mechanisms in the steel were taking into account: dislocation gliding with the particles and forest dislocations overcoming together with typical for the steel type structural inhomogeneities existence: the particle free zones. Proceeding from the steel real structure features, the particle overcoming by mobile dislocations was concluded to be the dominant strengthening mechanism in the steel. Hence the steel starting creep temperature was calculated which value is in accordance with the known for the Fe based alloys minimal temperature of the dislocation climbing beginning. Based on the obtained results and their fundamental theoretical background, possibility is emphasized to apply the approach in science, technology control, medicine etc