  In this study, we consider dark matter and dark energy as grand-canonical
systems which are open, non-equilibrium coupled, and interacting systems. For
the first time, we propose a new more realistic interaction scheme to explain
dynamics between coupled interacting thermodynamic systems. Based on this new
interaction schema, we propose new theorems to define the interactions
including mutual and self-interactions. We proved the theorems based on the
energy conservation law of thermodynamics. Furthermore, we obtain new coupled
equations using the theorems. We numerically solved the interaction equations
and obtained phase space diagrams and Lyapunov exponents. We show that the
interaction between dark matter and dark energy is chaotic. We conclude that
these theorems and results can be generalized to all coupled interacting
particle and thermodynamic systems. Finally, we evaluated that the obtained
results indicate the existence of a new law in physics. Additionally, based on
the results, we gave physical definitions of basic concepts such as chaos and
self-organization and pointed out the existence of hidden symmetries and
variables in interacting systems.
