1 hour ago, julius2 said:

Ok, entropy is probably about the degree of randomness. Ie. It doesn't necessarily have to increase.

Wherever you feel the urge to use the word 'randomness' in relation to entropy, try replacing it with 'diversity': diversity of position; diversity of momentum; diversity of type; and you will be much closer.

The 'diversity of type' (or 'entropy of mixing') is a much underappreciated aspect as it permits the creation of novel structures due to the low entropy ordering of the structure being offset by its high entropy contribution to diversity.

Hence stars can ultimately produce the heavier elements; which beget life; which begets the broken transistor radios and other miscellaneous items of space junk that continue to populate a cold universe at the end of time.

@MigL can possibly explain how all this structure can be eroded away in the apparent absence of the necessary activation energy - though I can't see it.

2 hours ago, julius2 said:

We are aware of time right now.....

So how can be that it “was never known”?

2 hours ago, julius2 said:

Like I said...."bizarre states"

E.g. all registered entities on the planet will have forgotten that time was existing

What, pray tell, is a registered entity?

You may see entropy from a Chemistry viewpoint @sethoflagos , I see it from a Physics viewpoint ( subtle difference ).
Entropy is a measure of the number of ways, or degrees of freedom, that energy/particles can be arranged in.
Maximal entropy is when all possible states are occupied and there are no further paths to other independent states.
I don't see the relevance of 'structures'.

I believe the Equipartition Theorem is a valid example

12 minutes ago, MigL said:

You may see entropy from a Chemistry viewpoint @sethoflagos , I see it from a Physics viewpoint ( subtle difference ).
Entropy is a measure of the number of ways, or degrees of freedom, that energy/particles can be arranged in.
Maximal entropy is when all possible states are occupied and there are no further paths to other independent states.
I don't see the relevance of 'structures'.

I believe the Equipartition Theorem is a valid example

How would a Physicist view the entropy of this isolated system ?

A small body m1 orbits a larger body m2 but remains under the influence of a third body m3 so the energy varies throughout the orbit of m1.

If the energy of the system has a path to another state ( an independent degree of freedom ) then that 'dilutes' the energy available, and entropy increases.
If there is no path to another state, then the system is in equilibrium at maximum entropy.

The example I previously used was proton decay, as we are not sure it can happen.
If it does decay ( no sooner than 10³⁴ years ), then it provides a path to another state, and proton decay may well provide the 'last' useable energy of the universe, before 'heat death'.

Since the orbit of m1 is continuous, there must be an infinite count of energy states, all different, ie a continuum of energy states.

1 hour ago, MigL said:

You may see entropy from a Chemistry viewpoint @sethoflagos , I see it from a Physics viewpoint ( subtle difference ).
Entropy is a measure of the number of ways, or degrees of freedom, that energy/particles can be arranged in.
Maximal entropy is when all possible states are occupied and there are no further paths to other independent states.
I don't see the relevance of 'structures'.

A 'maximal entropy' planet Earth would have no atmosphere-ocean-crust-mantle-core structure. It would be all mixed up into a homogenous blob (which is roughly how it started out).

Clearly, this was unstable as the denser components had way too much gravitational potential energy for underlying lower density material to support and they sank towards the centre despite the long-term reduction in (ISOTHERMAL) entropy that implied. The 2nd Law wasn't broken:: the large negative dU component of Free Energy was released as more than sufficient entropy increasing heat to offset the entropy reducing TdS drop in thermodynamically available states. But ultimately that heat, and its associated entropy, would be radiated off into space.

Far from evolving into an unstructured body of maximal entropy, it evolves toward a highly structured body of minimal free energy. (Since you're a physicist, I'm using Helmholtz Free Energy here 😉)

Similarly, life uses the surplus free energy of other 1st Law energy sources (sunlight, chemical energy) to convert high entropy water and carbon dioxide into highly structured lower entropy cells and multicellular bodies.

I use the word 'structure' here as a preferred alternative to 'negentropy' or 'complexity', both of which I think are easily misunderstood. But they are effectively synonyms for reservoirs of APPARENTLY negative entropy. I say 'apparently' since the negative residue is more than balanced by a corresponding radiation of heat from the system. Clearly these must be accounted for in any discussion of cosmological entropy budgets.

2 hours ago, MigL said:

The example I previously used was proton decay, as we are not sure it can happen.
If it does decay ( no sooner than 10³⁴ years ), then it provides a path to another state, and proton decay may well provide the 'last' useable energy of the universe, before 'heat death'.

Proton decay with a 10³⁴ year half-life would clearly obliterate all familiar structures within 10³⁵ years. I half suspect that the concept was invented by some physicist who couldn't be bothered to account for cosmological structures in his calculations. Let him demonstrate an unambiguous and spontaneous proton decay, and I might begin to take the possibility seriously. Until then, I shall remain commitedly atheist about it.

2 hours ago, studiot said:

How would a Physicist view the entropy of this isolated system ?

A small body m1 orbits a larger body m2 but remains under the influence of a third body m3 so the energy varies throughout the orbit of m1.

How would the energy vary at all? It’s a conserved quantity. The KE or PE individually would vary, but not the sum.

Thanks Swansont.
Was just about to reply that the energy states @studiot talks about

2 hours ago, studiot said:

Since the orbit of m1 is continuous, there must be an infinite count of energy states

are already occupied, and in equilibrium with gravity ( a conservative force ).
To access any other independent states, or degrees of freedom, you would need to add useable energy.

The same can be said for @sethoflagos planet and atmosphere example.
They are in equilibrium with gravity; where are the other independent states, or degrees of freedom, that are available ?

33 minutes ago, MigL said:

To access any other independent states, or degrees of freedom, you would need to add useable energy.

The same can be said for @sethoflagos planet and atmosphere example.
They are in equilibrium with gravity; where are the other independent states, or degrees of freedom, that are available ?

Yup, currently inaccessible states need a free energy boost to access them. No disagreement here.

Now how about properly addressing my comments on structure? Or am I just wasting my time?

59 minutes ago, sethoflagos said:

Now how about properly addressing my comments on structure?

I didn't think I had to ...

2 hours ago, sethoflagos said:

A 'maximal entropy' planet Earth would have no atmosphere-ocean-crust-mantle-core structure. It would be all mixed up into a homogenous blob (which is roughly how it started out).

Really ?
Is that the lowest energy state ?

2 hours ago, sethoflagos said:

this was unstable as the denser components had way too much gravitational potential energy for underlying lower density material to support and they sank towards the centre

Or is this ???

1 hour ago, sethoflagos said:

Or am I just wasting my time?

Not if we both learn something 🙂 .

7 hours ago, swansont said:

How would the energy vary at all? It’s a conserved quantity. The KE or PE individually would vary, but not the sum.

10 hours ago, studiot said:

How would a Physicist view the entropy of this isolated system ?

That is indeed the definition of an isolated system.

But that energy is distributed between KE and PE (partitioned) as you say so both must continually vary to preserve the sum.

This is exactly where consideration of the system, along with the system boundary, is necessary, as I also pointed out.

1 hour ago, studiot said:

That is indeed the definition of an isolated system.

But that energy is distributed between KE and PE (partitioned) as you say so both must continually vary to preserve the sum.

This is exactly where consideration of the system, along with the system boundary, is necessary, as I also pointed out.

But trading KE and PE is true in a two-body system as well.

8 hours ago, MigL said:

  10 hours ago, sethoflagos said:

A 'maximal entropy' planet Earth would have no atmosphere-ocean-crust-mantle-core structure. It would be all mixed up into a homogenous blob (which is roughly how it started out).

Really ?
Is that the lowest energy state ?

Really. All particles would be free to diffuse to any location within a planet of uniform composition.

And no. The lowest energy state would see the planet in an onion structure of concentric shells of pure components sorted by density. But this doesn't happen either.

(Glossing over issues rnvolving chemical potential: reaction, phase change, etc.)

The direction of planetary evolution is towards a state of lowest free energy, which is a hybrid of these two forces (H = U - TS) The U component drives differentiation of the planetary interior into shells of differing densities; the S component ensures that some degree of mixing always remains, especially among components of similar density.

9 hours ago, MigL said:

Not if we both learn something 🙂 .

Well, you've obliged me to think through in detail something that I'd only a vague hand-wavy picture of before, so thanks for that.

2 hours ago, swansont said:

But trading KE and PE is true in a two-body system as well.

...where TdS again characterises the minimum heat shed by the system due to tidal forces as the two bodies exchange angular momentum on their journey to becoming a fully tidally locked single structure.

Wouldn't this now become effectively a single isolated body?

1 hour ago, sethoflagos said:

...where TdS again characterises the minimum heat shed by the system due to tidal forces as the two bodies exchange angular momentum on their journey to becoming a fully tidally locked single structure.

Wouldn't this now become effectively a single isolated body

I’d assumed we were discussing only orbital mechanics in that scenario

13 hours ago, sethoflagos said:

Proton decay with a 10³⁴ year half-life would clearly obliterate all familiar structures within 10³⁵ years. I half suspect that the concept was invented by some physicist who couldn't be bothered to account for cosmological structures in his calculations. Let him demonstrate an unambiguous and spontaneous proton decay

As I understand it, theories going beyond the SM and not conserving baryon number would allow proton decay. GUTs e.g.

9 minutes ago, TheVat said:

As I understand it, theories going beyond the SM and not conserving baryon number would allow proton decay. GUTs e.g.

As I understand the thread, it is about the Heat Death, which is (was) a proposed consequence of very well established theories, from long before all the cosmological and standard model stuff, which still under development and far more speculative.

I was impressed with Seth's thinking on the subject. +1

13 hours ago, MigL said:

are already occupied, and in equilibrium with gravity ( a conservative force ).

Equilibrium is another of those concepts that are bandied about a bit to freely, without proper description/ definition of what is in equilibrium and what sort of equilibrium is meant static or dynamic, stable, unstable or metastable etc). Dynamic equilibrium for instance implies motion, which has implications for the proposed Heat Death.

I hope @julius2 is benefitting from the discussion, now you guys have the bit between the teeth.

1 hour ago, swansont said:

I’d assumed we were discussing only orbital mechanics in that scenario

That scenario was correctly introduced by @studiot as an example of long term low entropy structure in the universe.

Entropy is central to the OP, so one may wonder whether a lossless classical n-body system has any relevance. It appears to be a thermodynamic dead end. What I'm attempting to do is argue for the thermodynamic relevance not only of the path toward the minimum free energy classical ideal, but also the relevance of such structures as 'eternal' reservoirs of 'negentropy' (despite an aversion to that term).

1 hour ago, TheVat said:

As I understand it, theories going beyond the SM and not conserving baryon number would allow proton decay. GUTs e.g.

A parallel, but very much faster evolutionary path has been made for the condensation of protons from a primordial quark gluon plasma: another low entropy, minimum free energy structure created with a truly enormous generation of thermal energy to maintain consistency with the 2nd Law.

CERN may well suggest that breaking protons is commonplace, if one turns a blind eye to their need to create energy densities coequal to those of the early universe in order to achieve it. Taken together the 1st and 2nd Laws suggest that one cannot reverse the arrow of time in this way on a cosmological scale as proton decay implies. I'd sooner buy into astrology.

1 hour ago, studiot said:

Equilibrium is another of those concepts that are bandied about a bit to freely, without proper description/ definition of what is in equilibrium and what sort of equilibrium is meant static or dynamic, stable, unstable or metastable etc). Dynamic equilibrium for instance implies motion, which has implications for the proposed Heat Death.

Quite. +1

Edited June 17Jun 17 by sethoflagos
High entropy grammar

"It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems." - Lee Smolin

https://physicstoday.aip.org/features/time-laws-and-the-future-of-cosmology

Why are we even talking about maximal entropy systems where there is a source of useable energy ?

3 hours ago, sethoflagos said:

The lowest energy state would see the planet in an onion structure of concentric shells of pure components sorted by density. But this doesn't happen either.

It doesn't happen because the core provides energy ( radiative heat ) causing motion due to differential heating.
What does happen in a 'dead' asteroid is stratification according to density.
That's exactly how gravity works.

1 hour ago, studiot said:

proper description/ definition of what is in equilibrium and what sort of equilibrium is meant static or dynamic, stable, unstable or metastable etc)

Are we not discussing maximal entropy, as in the 'heat death' of the universe ?
A system in a state without flux of energy through its boundary, that is in its lowest possible energy would tend to, and eventually have no choice but, to be in equilibrium.
For such a state to be dynamic it would need an influx of energy.
For such a state to be unstable it would not be in its lowest possible energy.

Edited June 17Jun 17 by MigL

31 minutes ago, TheVat said:

https://physicstoday.aip.org/features/time-laws-and-the-future-of-cosmology

Love this. A metathesis combining Darwinian evolution with cosmological thermodynamics!

Perhaps we have the beginnings of an explanation for that image of a broken transistor radio at the end of a block universe that's haunted me since H2G2 first aired.

14 minutes ago, MigL said:

It doesn't happen because the core provides energy ( radiative heat ) causing motion due to differential heating.

Gravitational stratification occurs without this surplus free energy as it releases enough heat to activate the process on its own. Decaying nucleides merely help accelerate the process. I omitted them for brevity.

19 minutes ago, MigL said:

What does happen in a 'dead' asteroid is stratification according to density.
That's exactly how gravity works.

We're saying the same thing.

21 minutes ago, MigL said:

Are we not discussing maximal entropy, as in the 'heat death' of the universe ?

Here's the paradox:

The universe as a whole progresses through states of ever increasing entropy in conformance with the 2nd Law.

Bound matter progresses through states of ever decreasing free energy into low entropy structures.

Conformance with 1st & 2nd Laws requires that theoretical 'Maximum Entropy' states are eternally unavailable.

That broken transistor radio remains viable.

10 minutes ago, sethoflagos said:

Bound matter progresses through states of ever decreasing free energy into low entropy structures.

The ultimate bound state is a Black Hole.
BHs do not lower entropy; information is 'stored' in Planck-sized domains on the surface of the Event Horizon, in accordance to the Bekenstein-Hawking relation.
It is this dynamic equilibrium ( making Studiot happy ) that accounts for BHs having a characteristic temperature, and therefore, black body ( Hawking ) radiation, as there is a flux through the surface of the EH.
The 'final' equilibrium is when the BH evaporates.

Similarly, should protons decay into fundamental particles, so will neutrons as they have nothing to keep them happy in nucleii. So no atoms.
Yeah, no transistor radios at the end of the universe.

26 minutes ago, MigL said:

The ultimate bound state is a Black Hole.
BHs do not lower entropy; information is 'stored' in Planck-sized domains on the surface of the Event Horizon, in accordance to the Bekenstein-Hawking relation.

I also omitted Black Holes for simplicity (and also they're not in my field).

However, I see them as a special kind of structure where the heat generated by infalling matter cannot escape the event horizon making them rather skin to miniuniverses of their own.

Of course, I've come across Hawking radiation which rather muddies this comfy little rationalisation, but then one has the apparent loss of quantum information to explain. I suspect the 2nd Law will survive intact.

38 minutes ago, MigL said:

Similarly, should protons decay into fundamental particles, so will neutrons as they have nothing to keep them happy in nucleii. So no atoms.
Yeah, no transistor radios at the end of the universe.

Do you gain spiritual comfort from the thought? 😄

1 hour ago, sethoflagos said:

Here's the paradox:

The universe as a whole progresses through states of ever increasing entropy in conformance with the 2nd Law.

Bound matter progresses through states of ever decreasing free energy into low entropy structures.

Conformance with 1st & 2nd Laws requires that theoretical 'Maximum Entropy' states are eternally unavailable.

Is the bound matter closed system?

I think you’re only looking at a subset; in creating a low entropy structure you are sending the (systems with) high entropy elsewhere.

Does maximum entropy require every subsystem have maximum entropy?

15 minutes ago, swansont said:

Is the bound matter closed system?

No. At least it's certainly not adiabatic: except for black holes (within limits), thermal energy is free to escape the system.

19 minutes ago, swansont said:

I think you’re only looking at a subset; in creating a low entropy structure you are sending the (systems with) high entropy elsewhere.

Follows naturally from the above.

21 minutes ago, swansont said:

Does maximum entropy require every subsystem have maximum entropy?

If it were thermodynamically available (for reasons given in my last post, I can't see how it can be) then one would (depending on where you're prepared to draw the line of incredulity) have to accept that all subsystems upstream of that line would dissipate.

There are near-infinitely more ways of redistributing the hadrons of the earth-moon system than their current state. If as @MigL insists, even the hadrons are up for grabs, then we're in some sort of featureless Penrose land.