The backbone of non-equilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and stable ones survive. The physical concepts from the stability structure and the related formalism of constrained entropy inequality are universal by construction. Therefore, the mathematical tools and the physical concepts of thermodynamics help formulate dynamical theories of any systems in social and natural sciences. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.
Keywords: Lyapunov stability; absolute temperature; evolution equation; non-equilibrium thermodynamics; universality.