• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,731 comments
1,470 users with positive rep
818 active unimported users
More ...

  Questioning Stability.

+ 2 like - 0 dislike

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?

asked Oct 17, 2016 in General Physics by Naveen (85 points) [ no revision ]
recategorized Oct 18, 2016 by Dilaton

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!

1 Answer

+ 3 like - 0 dislike

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 Arnold Neumaier (15,787 points) [ revision history ]
edited Oct 19, 2016 by Arnold Neumaier

@Arnold Neumaier thanks for the answer!

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights