Vacuum of Space and the 2nd Law of Thermodynamics

There is a flawed reasoning behind the 2nd Law of Thermodynamics (2LoT) being used to disprove the existance of vacuum in space. A "gas filling up the available space" is just an example of a spontaneous process explained by the 2LoT; more importantly, is not a statement of the 2LoT.

A crucial element when analyzing the Earth-Atmosphere-Space system is the effect of the gravitational force on the atmosphere. Disconsidering the gravitational force, the Atmosphere-Space system would not make up an isolated system (which is a requirement of the 2LoT for an entropy increase dS >= 0)

References:
- https://www.thermal-engineering.org/what-is-second-law-of-thermodynamics-definition/
- https://en.wikipedia.org/wiki/Second_law_of_thermodynamics
- https://faculty.fiu.edu/~mebela/chm3410_chapter4.pdf
- http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/barfor.html