Setting up the physical principles of resilience in a model of the Earth System

Resilience is a property of social, ecological, social-ecological and biophysical systems. It describes the capacity of a system to cope with, adapt to and innovate in response to a changing surrounding. Given the current climate change crisis, ensuring conditions for a sustainable future for the habitability on the planet is fundamentally dependent on Earth System (ES) resilience. It is thus particularly relevant to establish a model that captures and frames resilience of the ES, most particularly in physical terms that can be influenced by human policy\footnote{See page 4 for examples of strategies}. In this work we propose that resilience can serve as a theoretical foundation when unpacking and describing metastable states of equilibrium and energy dissipation in any dynamic description of the variables that characterise the ES. Since the impact of the human activities can be suitably gauged by the planetary boundaries (PBs) and the planet's temperature is the net result of the multiple PB variables, such as $\text{CO}_2$ concentration and radiative forcing, atmospheric aerosol loading, atmospheric ozone depletion, etc, then resilience features arise once conditions to avoid an ES runaway to a state where the average temperature is much higher than the current one. Our model shows that this runaway can be prevented by the presence of metastable states and dynamic friction built out of the interaction among the PB variables once suitable conditions are satisfied. In this work these conditions are specified. As humanity moves away from Holocene conditions, we argue that resilience features arising from metastable states might be crucial for the ES to follow sustainable trajectories in the Anthropocene that prevent it run into a much hotter potential equilibrium state.