. Here's a quotation from "Quora":

|The vacuum expectation value of the Higgs field is just the
|value that we would "expect" it to have when it is in its
|vacuum state, which is the state of lowest energy. It turns
|out that it is a general law of nature that physical systems
|always "want" to be in the state of lowest possible energy.
|The allowed values for the energy are determined by the
|system's potential energy function. In the case of the Higgs
|field, the potential function looks (more or less) like this

. My question is not about Higgs fields, but I'd like to focus
on this part:

|It turns out that it is a general law of nature that physical
|systems always "want" to be in the state of lowest possible
|energy.

. "Want" is not a very appropriate term in physics. But

- is there really such a law? And if so,

- how can one interpret this law in the way that the system
"wants" to be in the state of the lowest possible energy?

- If a system tries to get into a state of lowest energy,
the only place it can give its energy to is another system,
which also wants to get into a state of lowest energy . . .
So it seems that the two systems are in a fight, each one
trying to force its energy upon the other system then.
What determines which system wins this fight?

On 2024-06-18 18:25:10 +0000, Stefan Ram said:

> . Here's a quotation from "Quora":
>
> |The vacuum expectation value of the Higgs field is just the
> |value that we would "expect" it to have when it is in its
> |vacuum state, which is the state of lowest energy. It turns
> |out that it is a general law of nature that physical systems
> |always "want" to be in the state of lowest possible energy.
> |The allowed values for the energy are determined by the
> |system's potential energy function. In the case of the Higgs
> |field, the potential function looks (more or less) like this
>
> . My question is not about Higgs fields, but I'd like to focus
> on this part:
>
> |It turns out that it is a general law of nature that physical
> |systems always "want" to be in the state of lowest possible
> |energy.
>
> . "Want" is not a very appropriate term in physics. But
>
> - is there really such a law? And if so,

Not exactly. The law is that entropy always increases, which means
that energy becomes more evenly distributed. Therefore, when there
is much energy consentrated in one place, that place tends to lose
a part of its energy to places that have less. The result is that
any small part of the unverse is most of its time in its lowest
energy state.

--
Mikko

Mikko <mikko.levanto@iki.fi> wrote or quoted:
>On 2024-06-18 18:25:10 +0000, Stefan Ram said:
>>. Here's a quotation from "Quora":
.. . .
>>|It turns out that it is a general law of nature that physical
>>|systems always "want" to be in the state of lowest possible
>>|energy.
.. . .
>Not exactly. The law is that entropy always increases, which means
>that energy becomes more evenly distributed.

The heat death (the conversion of all forms of energy into
heat energy) is rather something long-term, but one can also
be interested in the dynamics within shorter periods of time.

At the system boundaries, the flow of extensive quantities
is determined by the difference of the intensive quantities
(potentials).

Thus, (positive) electric charge (extensive quantity)
flows, for example, from the system with the higher
electric potential (intensive quantity) to the system
with the smaller electric potential.

Yes, and in doing so, the total energy in the two systems would
become smaller. But since energy must not be destroyed, it must
be converted into another form. If the systems cannot exchange any
other forms of energy, then only the generation of entropy remains.
And it then flows rather to the colder of the two systems.

So you were right insofar as one must take entropy into account.

Here is the formulation with potential differences, once without
and once with "want":

Without "want": When two systems come into contact, an extensive
quantity flows to the system with the smaller associated potential.

With "want": Every system wants to give off its extensive
quantities (which reduces its energy), but this is only
possible if the system finds another system in which the
potential associated with the extensive quantity is smaller.

If we regard a system with a small potential as "weak"
and a system with a large potential as "strong", we can say
that every system wants to impose its energy in the form of
extensive quantities on other systems, but it only succeeds
in doing so if it finds a weaker system.

The concept of the thermodynamic potential, which determines
the direction of the flow of extensive quantities, was still
missing from your explanations.

(I'm not particularly interested in the Higgs field itself, as
I wrote, but if I imagine the Higgs field and another field, and
each wants to give away its energy, then I can't find suitable
forms of energy with their associated extensive and intensive
quantities that would help me predict the temporal evolution.)