The consistent numerical treatment of the balance laws in multi-physical systems requires specialized time integration schemes. These integrators should preserve the invariants of the system, as dictated by Noether’s theorem, while adhering to the fundamental laws of thermodynamics. That is, the time- stepping schemes should conserve momentum maps corresponding to the symmetries of the systems, conserve energy, and ensure non-decreasing entropy for closed systems. The GENERIC (General Equa- tion for Non-Equilibrium Reversible-Irreversible Coupling) is a two generator formalism which provides the foundation for constructing such integrators for (closed) discrete systems. As a first model problem, a thermo-visco-elastic pendulum under large deformations is considered [1]. Thus, integrators must cope with viscous dissipation and heat exchange. Energy-Momentum-Entropy schemes are developed for the model problem, and their energy and entropy consistency is shown. The use of temperature, en- tropy, internal energy, or total energy as independent thermal variables is discussed. The focus is on the special form of GENERIC according to Mielke [2], and the introduction of auxiliary variables such as strain-type quantities. Extending the model problem to include electromagnetic forces enables a broader applicability to coupled electro-mechanical or magneto-mechanical systems, which are critical in modern engineering applications. The development of GENERIC-based integrators for discrete systems can be seen as a preparatory step towards the development of GENERIC-based methods for corresponding coupled continuum problems. The extension of GENERIC towards open systems as a tool for control is presented by extending the GENERIC-framework in the spirit of port Hamiltonian (pH) systems. As a model problem, a simplified lumped parameter model of a microfluidic pump (see Franke et al. [3]) subjected to mechanical, thermal, and electrical loads is discussed. REFERENCES [1] V. Valdes y Beck, P. Betsch. Energy-Momentum-Entropy consistent time integration of dissipative thermomechanical systems in an extended framework of GENERIC. Proceedings in Applied Mathematics and Mechanics 23, e202200126 (2023). [2] A. Mielke. Formulation of thermoelastic dissipative material behavior using GENERIC. Continuum Mechanics and Thermodynamics 23, 233–256 (2011). [3] M. Franke, F. Z¨ahringer, M. Hille, R. Ortigosa, P. Betsch, A.J. Gil. A novel mixed and energy–momentum consistent framework for