# Energy vs Stability: Exploring Relationship & Understanding Stability

• Cole A.
In summary, a system's stability corresponds to its energy level. The driving force for stability is the tendency for a system to move toward the lowest possible energy state.
Cole A.
I'm having trouble understanding the relationship between a system's energy level and its stability (in a general sense).

My understanding is that chemical and physical systems experience a driving force that pushes them toward the lowest possible energy state (ignoring quasi-steady states and those things). Biochemistry calls this the Gibbs energy of reaction when the systems are chemical. The driving force represents the amount of non-PV (or useful) work that might be done by the system in moving toward that lowest energy level, and thus the system does the max amount of non-PV work by moving from an arbitrary energy level to the Gibbs energy minimum, or the energy level characterized by

$$\begin{equation*} \frac{dG}{dt} = 0. \end{equation*}$$

But I do not understand why the driving force exists (i.e. why it is favorable thermodynamically for a system to minimize its free energy). In other words, I cannot tell from the the laws of thermodynamics why natural systems tend toward lowest energy states.

And I also do not understand why a stable system corresponds to a low-energy one. My engineering prof. calls the state of lowest energy the state of maximum stability. Stability is a term that is tossed around a lot it seems, but I don't really understand what it means.

P.S. If the best answer would be something along the lines of "take a proper thermodynamics course," that would be fine.

Thanks

Your picture is a little incomplete that's all.
But I do not understand why the driving force exists (i.e. why it is favorable thermodynamically for a system to minimize its free energy).
It is statistical - it is easier to go at random to a lower energy than a higher one for a similar reason that it is easier to randomly get a pile of sand than a sand-castle. The "driving force" is kind-of a blanket term to cover "whatever it is about the system that tends to shift it from stability" which sounds like a circular definition doesn't it? See below.
I also do not understand why a stable system corresponds to a low-energy one.
The instability of a system is it's propensity to move away from it's previous state if it is given a little nudge.

A high energy state for a stationary ball would be on top of a hill. Give it a nudge and it rolls to the bottom of the hill - keeps going until it finds a depression, then it kinda rocks back and forth for a bit. So the depression is a lower energy state and stable.
The driving force in this system would be gravity - mainly. The ball won't spontaneously roll to the top of a hill because there are other, dissipative, forces too - it makes a noise, heats up, shifts bits of the scenery it bumps into on it's way, that sort of thing. Taken together, all these things give the ball a "tendency to try to get to the lowest energy state available".

The ball can sit in an identical geometry bowl and be stable at any height though... it may require more than a nudge of energy to get it out of the higher bowl - but once out the ball rolls to the lower bowl (there will be a highly unstable point where it could go either way). The "more than a nudge of energy" would be the reaction energy in chemistry - you have to give paper a bit of energy to start it burning but, once going, it will burn completely all by itself.

That help?
If the best answer would be something along the lines of "take a proper thermodynamics course," that would be fine.
That would help - but even then a decent picture does not emerge until you start to contemplate postgraduate work. You are still at the stage of using the results rather than working the underlying math.

I agree with Simon.
As an example, in classical mechanics, when you have a particle in a central potential V(x), the force excerted to it will be:
F=-dV/dx
Stability means that F=0, so dV/dx=0, V(x) is in a minimum or a maximum.
However, when V(x) is in a maximum ( d(dV/dx)/dx<0), then a small pertrubation will lead the system in instability ( F#0). When, on the other hand, V(X) is in a minimum, every small pertrubation will lead it to oscillate back and forth from the minimum like an harmonic oscillator, and it will eventually return there. Thus, minimum potential energy equals greatest stability.

thanks e.chaniotakis - I'd just want to add that the oscillations die down only if there are losses in the system. The dissipation of kinetic energy is what provides the tendency to seek the lowest energy.

It would be nice to get some feedback from OP...(?)

I'm sorry for my lack of feedback.

The instability of a system is it's propensity to move away from it's previous state if it is given a little nudge.

This one line provided a great deal of clarification. I appreciate your input, both of you.

## 1. What is the definition of energy and stability?

Energy refers to the ability to do work or cause change. It exists in many forms, such as kinetic, potential, thermal, and chemical energy. Stability, on the other hand, refers to the state of being steady, balanced, and resistant to change.

## 2. How are energy and stability related?

The relationship between energy and stability is complex. In general, higher energy levels in a system tend to lead to lower stability, as there is more energy available to cause change. However, in some cases, high energy states can also lead to increased stability, such as in the case of chemical bonds.

## 3. How do scientists study the relationship between energy and stability?

Scientists use various methods, such as experiments, simulations, and mathematical models, to study the relationship between energy and stability. They also analyze data and observe real-world phenomena to gain a better understanding of this relationship.

## 4. Can energy and stability be balanced?

Yes, it is possible for energy and stability to be balanced. In some systems, there is an optimal level of energy that results in maximum stability. This balance is essential for the functioning and survival of living organisms.

## 5. How does understanding the relationship between energy and stability benefit us?

Understanding the relationship between energy and stability is crucial in various fields, such as chemistry, biology, and physics. It can help us predict and control reactions and processes, develop new technologies, and improve our understanding of the natural world.

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