# Questioning Stability.

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Today in class my professor was explaining deeply about meta stability of an atom. This made me question,"why stability". Yes of course that is when a system has the least entropy and minimises its energy loss. But I cannot understand why the should a system be stable. What is the real meaning of stability?And why do objects ,when left free, tend to a state or position were they are stable all the time?

Note: I am questioning the very root of-"why stability?" ,not -"why do objects become stable?"And I am fully aware of the explanations regarding entropy and minimisation of PE. When we can understand the meaning of stability as its a state when our bodies would conserve energy, but how do particles like electrons and atoms know the same.Is there any theory regarding the question?

recategorized Oct 18, 2016

The stability is somehow a low frequency of state changes. For a given energy distribution, you will get changes when the values are often over the limits leading to change each state. However, these limits increase by accumulation as a simple Markov chain may show ( objects stay more time in big holes ). And when the limits increase by this mechanism, the occurences of energy levels needed for states changes become fewer. The system converges to a not absolute local minima ... which may be disturbed by  a quantum rare high level, and then starting the convergence to another minima. For rigourous maths, read the Cedric Vilanni "Convergence to equilibrium: Entropy production and hypocoercivity (pdf 2001) "  that clearly shows that elements hadn't to know anything leading to the measure of the emergent stability.

@igael Thanks a lot for your help!

"why stability". Yes of course that is when a system has the least entropy

No. A least entropy state is almost never stable!

Finally this question is not so naive from a @Naveen already aware of the maths :) Sorry for my previous comment but the links are really fine. I was just reading them again and again. I wonder how to show exactly that the stability is always what we call stable and that the nature ( not the maths ) has not chosen another stable value , for example, a minimum level of instability with our words. I hope to get the maths to be less lowbrow ...

@igael I did try to study the article that you had given a link to. Although I did understand a part of it, the math prevented me from understanding the crux of the article. If you could, please do simplify it for me( not sans the math but with enough physical significance that the math tries to communicate). Thanks!

Sorry, I cannot shorten ( unable ) a so dense document. It's not only the proof of convergence to equilibrium with less constrained models, it is also a review of the recent works on the question, not only on its thermodynamics aspects. You may start the first reading on page 11 §1.3 and see the table page 17. In fact, a little confused, I wonder if the answer to your question is not , in short, the fact that nature has some symmetries and not others... If you find that there is a kind of circularity around the atom metastability interpretation case, please develop.

@igael Sure, thanks!

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In Nature, energy dissipates to unobservable degrees of freedom that cannot be modelled (except in a very simplified way). As a consequence, the free energy of a bounded system with constant boundary conditions loses free (i.e., in principle observable) energy until everything is lost that can be lost (which is constrained through the laws of physics, embodied in the form of a free energy function as a function of the state).

Thus the state of such a system will end up in a local minimizer of the free energy surface. Such a state is called a stable state if the probability of being excited by enough energy to reach another local minimizer is tiny enough, and a metastable state otherwise.

Thus in the end, stability is a consequence of the fact that the free energy is bounded below and states of sufficiently low free energy are confined to compact regions of the state space. (Systems where these conditions are not met are typically not stable.)

answered Oct 19, 2016 by (15,747 points)
edited Oct 19, 2016

@Arnold Neumaier thanks for the answer!

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