  Once carbon emission neutrality and other sustainability goals have been
achieved, a widespread assumption is that economic growth at current rates can
be sustained beyond the 21st century. However, even if we achieve these goals,
this article shows that the overall size of Earth's global economy is facing an
upper limit purely due to energy and thermodynamic factors. For that, we break
down global warming into two components: the greenhouse gas effect and heat
dissipation from energy consumption related to economic activities. For the
temperature increase due to greenhouse gas emissions, we take 2 {\deg}C and 5
{\deg}C as our lower and upper bounds. For the warming effect of heat
dissipation related to energy consumption, we use a simplified model for global
warming and an extrapolation of the historical correlation between global gross
domestic product (GDP) and primary energy production. Combining the two
effects, we set the acceptable global warming temperature limit to 7 {\deg}C
above pre-industrial levels. We develop four scenarios, based on the viability
of large-scale deployment of carbon-neutral energy sources. Our results
indicate that for a 2% annual GDP growth, the upper limit will be reached at
best within a few centuries, even in favorable scenarios where new energy
sources such as fusion power are deployed on a massive scale. We conclude that
unless GDP can be largely decoupled from energy consumption, thermodynamics
will put a hard cap on the size of Earth's economy. Further economic growth
would necessarily require expanding economic activities into space.
