# If the energy of an ant is smaller than an elephant, does that mean the ant is more stable than the elephant?

I know that when a system is in its lowest level of energy, it is most stable. However, what if system 1 has lower energy than system 2, does it keep meaning so? Or do we need to examine their binding energies of them? If the systems have only two bodies, easy: the one which has lower binding energy is stabler because their bodies don't need so much energy to combine them ($E_{binding}=E_{total}-E_A-E_B$). But what about many-body systems? If the binding is only meaningful in the context of two, then what is the subtraction $E_{total}-E_A-\sum_i{E_i}$?

By saying "more stable", I mean that it is "easier to combine", not "more energetic".

• The its in "When a system is in its lowest level of energy, it is most stable" is crucial. From comparing the energy content of two different systems you don't learn anything about their comparative "stableness" (where average lifetime is probably the measure you have in mind, right?) – ACuriousMind Jul 4 '14 at 13:45
• The energy you are talking about is the binding energy ? To extend this concept to a many body system, you should use the chemical potential, that is the energy required to add an extra particle into a system. – Tom-Tom Jul 4 '14 at 13:51
• @ACuriousMind: I don't know if average lifetime is exactly what I meant to say. What I mean is like the gravitation between the sun and the earth: how do they binding with each others. Can you tell me more about "comparative stableness"? – Ooker Jul 4 '14 at 14:56
• Yes, it's a binding energy. Although my problem is actually need to use free energy, but I just ask a simpler question about energy in general. You can say that I'm thinking about the sun, the earth and the moon. They also don't have volume and hard to use statistical physics. – Ooker Jul 4 '14 at 14:59
• @ACuriousMind is absolutely right. A system is most stable in its least energetic state. If energy of system 1 is less than energy of system 2, it doesn't necessarily mean 1 is less stable than 2. Anyway, we cannot measure the internal energy of a system. So, it is impossible to compare the net energy of 2 systems. – ShankRam Dec 11 '15 at 13:23