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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".

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    $\begingroup$ 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?) $\endgroup$
    – ACuriousMind ♦
    Commented Jul 4, 2014 at 13:45
  • $\begingroup$ 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. $\endgroup$
    – Tom-Tom
    Commented Jul 4, 2014 at 13:51
  • $\begingroup$ @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"? $\endgroup$
    – Ooker
    Commented Jul 4, 2014 at 14:56
  • $\begingroup$ 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. $\endgroup$
    – Ooker
    Commented Jul 4, 2014 at 14:59
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    $\begingroup$ @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. $\endgroup$
    – ShankRam
    Commented Dec 11, 2015 at 13:23

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I guess that you should not compare them with each other. in fact stability is not a real thing. we know that when a system has potential energy it has ability to do work and turn them to kinetic energy so that its velocity will be increased and as we know velocity(not important velocity of particles or bigger masses)means that system is not stable(because of motion). so if you want to compare elephant and ant you have to comare their velocity after their potential energies turned to kinetic energy

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