On the scale we are talking there's only three sources of heat:
- The Sun
- Heat left from the formation of the Earth
- Heat of radioactive decay
The last two do not fluctuate and are minuscule compared to the sun and an order of magnitude smaller than Earths energy imbalance.
The sun we
actually directly measure.
(I'll hide the evidence so as not trigger imported taj)
We also directly measure the outgoing radiation:
When we compare the two they suggest that the Earth is receiving more energy than is leaving.
When we add up the energy stored in the land, ocean and atmosphere we see increasing amounts of heat. Confirming an imbalance.
(Wiki)
Most of the data confirming climate change is directly measured.
For other planets we directly measure the temperature with telescopes or probes.
Sure can. The difference help show the impact of an atmosphere.
Since you aren't using the commonly accepted definition of thermodynamics you need to clarify what you mean by processes.
All chemical process are driven either by the energy originally from the sun or geothermal heatflux.
Same with biological changes. They change the Earths albedo or they change the chemical composition of the atmosphere all of which are measurable and being measured.
Per NASA
Look why don't you check out this link to the American Chemical Society Climate Science Toolkit.
https://www.acs.org/content/acs/en/climatescience.html
It goes into detail on how the climate works and is measured.