Subject: Is a 'terrestrial' planet's lifetime determined by it's mass?

By terrestral I mean solid like the inner planets of the solar system.
Is a planet's geologic activity limited by it's mass?
Planets are geologically active because of the energy produced from the 
pressure of it's own mass on it's core melts the surrounding rock, as 
planets dissapate heat through volcanic activity and outgassing, do they 
lose their atmosphere due to molecules being destroyed by solar radiation 
and the resulting light(not heavy)atoms or diatomic molecules escaping 
into the atmosphere, as they are no longer being replenished by volcanic 
activity or by the now dwindling biology on the planet(assuming it 
existed)?
Is this what caused Mars to turn out how it did?
Maybe it was earth-like in the past, but it cooled off faster because of 
its low mass.
If this is the case, how long would it take for Earth to "cool down?"
Thank you for considering my long question.
-Matt

Re: Is a 'terrestrial' planet's lifetime determined by it's mass?