Primarily released by the conversion of primary fossil energy sources, anthropogenic greenhouse gas emissions influence global warming fundamentally. Since they enable increasing the share of sustainable energy sources in the energy supply and reducing greenhouse gas emissions through targeted integration, power-to-X technologies promise to be an important element of compliance with impending regulations and laws. VDI 4663 guideline for strategically optimizing (technical) processes applies the physical optimum, a promising performance indicator for a unified, time-independent, and structured evaluation of power-to-X technologies that defines an operation under physically optimal conditions as a limit value. This study applies VDI 4663 to a power-to-X system and evaluates different components. It specifically examines current power-to-gas applications, the physical optimum as a limit-oriented indicator and its application to complex processes, the physically optimal operation of electrolysis and methanation, heat transfer as a critical component of methanation, the evaluation of a heat exchanger based on the physical optimum, and targeted process optimization based on VDI 4663. The outcome is an energy index for the evaluation of a heat exchanger, factoring in its structural design. The physical optimum of electrolysis and methanation developed here can also be employed as the basis for targeted optimization. This study serves as a basis for the evaluation of other power-to-X systems and introduces the application of VDI 4663. Additionally, the applicability of the physical optimum to chemistry-based processes is validated.