[Bored chemist]

The key concepts here are fluctuation

What fluctuations?
How long do they last?

[hamdani yusuf (OP)]

The key concepts here are fluctuation

What fluctuations?
How long do they last?

Kinetic energy of each molecule is supposed to fluctuate over time.
The fluctuation keeps going even without phase transition.

[Bored chemist]

How long do they last?

[hamdani yusuf (OP)]

How long do they last?

as long as the system exists.

[Bored chemist]

How long does each fluctuation last?

[hamdani yusuf (OP)]

How long does each fluctuation last?

does it really matter?

[Bored chemist]

How long does each fluctuation last?

does it really matter?

If if didn't matter I wouldn't be asking you for a fourth time...

[hamdani yusuf (OP)]

How long does each fluctuation last?

does it really matter?

If if didn't matter I wouldn't be asking you for a fourth time...

What difference would it make if it lasts for less than 1 nanosecond instead of more than 1 ns?

[chiralSPO]

What difference would it make if it lasts for less than 1 nanosecond instead of more than 1 ns?

If we were to view the system at such a fine resolution that we could observe extremely short fluctuations (ie 10^–20 seconds), then the ice could be interpreted as being in equilibrium with superheated plasma (due to the Heisenberg Uncertainty relationship of time vs energy, which can be demonstrated as physically "real" and meaningful by the broad spectrum of ultrafast lasers).

As has been pointed out numerous times in this thread: temperature and equilibrium are emergent properties of large systems, and deal with things like averages. You will get into trouble by trying to extend these concepts to individual molecules. There isn't any meaningful definition of temperature for a single molecule. Likewise, there is no meaningful difference between solid or liquid for a single molecule.

We can look at the whole bulk system (many molecules, with macroscopic spatial and temporal resolution) and talk about temperature, equilibrium, phase, entropy, enthalpy etc., using classical physics/thermodynamics.

Or we can take a molecular/atomistic view, and look at small collections of molecules, in which case we will need to use quantum theories.

We can't try applying both models—this leads to nonsensical answers.

[alancalverd]

There will always be molecular interchange at the interface between ice and water because the ensemble is not at 0K, but as you have defined them at the same temperature, there will be no NET exchange of energy.

[Eternal Student]

Hi.

   If I recall, there was a situation described by someone (Hamdani?) earlier.
There was a container insulated to the outside world but with a barrier between two inner regions.  The barrier allowed thermal contact between the two regions.    Region I was filled with mainly ice (and let's say some liquid water to ensure good thermal contact) at 0 deg C.     Meanwhile, Region II was filled with mainly liquid water at 0 deg C.  So everything is held at 0 deg. C on a macroscopic scale.
    If the barrier is a perfect insulator then the reasonable expectation of microscopic random interactions is that some melting and some freezing will occur in each region, it's just that overall there's no net change.   However, the barrier is a problem because it can pass energy over to the other region if a phase change occurs close to the barrier.
   There is more ice in region I so, just by the assumption of random phase shifts on a microscopic scale, melting happens more often in region I than in region II  (and conversely freezing is more frequent in region II than region I).  Over time, I would expect an equilibrium to be reached where there is an equal proportion of ice and liquid in both regions. 
   That does mean that a significant proportion of the originally liquid region has frozen while a significant amount of the icy region has melted:  There has been a net transfer of energy (latent heat) from one region to the other.
    (I've never actually done the experiment, just seems reasonable).

   Also, on a minor note:  Water changes density when freezing.  I've been ignoring pressure and volume changes. 
   
Best Wishes.

[Bored chemist]

How long does each fluctuation last?

does it really matter?

If if didn't matter I wouldn't be asking you for a fourth time...

What difference would it make if it lasts for less than 1 nanosecond instead of more than 1 ns?

Given that all the molecules in a crystal are moving, how long does it take before you know if it has melted?

Do you know that diffusion takes place in solids?

[hamdani yusuf (OP)]

There will always be molecular interchange at the interface between ice and water because the ensemble is not at 0K, but as you have defined them at the same temperature, there will be no NET exchange of energy.

Yes, but there's different phase between left and right side of the separator, hence difference in internal energy.

A rotating magnet and an aluminum disk can have the same initial temperature. But when they are brought close to each other, some temperature increase is observed on the aluminum disk.

[hamdani yusuf (OP)]

We can look at the whole bulk system (many molecules, with macroscopic spatial and temporal resolution) and talk about temperature, equilibrium, phase, entropy, enthalpy etc., using classical physics/thermodynamics.

Or we can take a molecular/atomistic view, and look at small collections of molecules, in which case we will need to use quantum theories.

We can't try applying both models—this leads to nonsensical answers.

But we can observe the changes in the system, if any.
It's either some ice in the left side melts or it doesn't.
It's either some water in the right side freezes or it doesn't.

[hamdani yusuf (OP)]

Given that all the molecules in a crystal are moving, how long does it take before you know if it has melted?

If there is energy flow, then after an hour or so I should be able to see some water in the left side of the container, which is previously filled with ice. Some ice would be formed in the right side.
If there is no energy flow, then after a day I should only still find ice in the left side of the container. The right side should still contain water.

[hamdani yusuf (OP)]

There is more ice in region I so, just by the assumption of random phase shifts on a microscopic scale, melting happens more often in region I than in region II  (and conversely freezing is more frequent in region II than region I).  Over time, I would expect an equilibrium to be reached where there is an equal proportion of ice and liquid in both regions.
   That does mean that a significant proportion of the originally liquid region has frozen while a significant amount of the icy region has melted:  There has been a net transfer of energy (latent heat) from one region to the other.
    (I've never actually done the experiment, just seems reasonable).

It seems reasonable to me too.

Also, on a minor note:  Water changes density when freezing.  I've been ignoring pressure and volume changes.

Consider the container is flexible enough to keep in touch with its contents, hence maintaining the pressure while the volume is changing.

[Eternal Student]

Hi.

Consider the container is flexible enough to keep in touch with its contents, hence maintaining the pressure while the volume is changing.

   Sadly, that's still a minor issue.   Work,  pΔV,   is done on a system if there's a volume change ΔV  while maintaining constant pressure p.
   If you want to avoid doing work on either region (and effectively changing the internal energy of the material in that region), then I think you must have a rigid container where the volume is held constant.  Inevitably then the pressure of both regions will start to change and this will oppose the freezing in region II and the melting in region I.   However, the effect probably won't be too important.  Overall the proportion of ice-to-liquid won't end up being exactly the same in both regions BUT there will still have been some net freezing in region II and net melting in region I.

- - - - - - - - - - - - -
    I think the point made by others  ( @Bored chemist  and @chiralSPO  for example)  is good and worth mentioning again.    Temperature is an extremely difficult thing to define.   It's a macroscopic property not a microscopic property.   As such temperature and most of thermodynamics only applies to large scales and average actions of particles in large bodies.
    In practice, a barrier that allows idealised thermal energy transmission is a practical impossibility.  A real barrier allows energy flow based solely on the local regions that are in the vicinity of the barrier.   It would allow a net flow of energy when there is some localised atypical region next to the barrier  (causing what looks like a local temperature gradient from one side to the other).   You can't physically build a suitable barrier that will sample the wide-scale temperature of everything in region I and compare that to the wide-scale temperature in region II and only allows energy to pass if those wide-scale temperatures show a difference.
   So, yes, in practice you can get a net transfer of energy from an icy region to a liquid region when they are at the same temperature but only because the barrier is not idealised and a temperature is just a wide-scale average property, it does not prevent a localised atypical patch forming close to the barrier.

Best Wishes.

[hamdani yusuf (OP)]

Sadly, that's still a minor issue.   Work,  pΔV,   is done on a system if there's a volume change ΔV  while maintaining constant pressure p.

Where does the energy come from, and where does it go to?

Here is what I found in Wikipedia. Does it also apply to liquid and solid?

https://en.wikipedia.org/wiki/Work_(physics)#Work_by_a_gas

Where P is pressure, V is volume, and a and b are initial and final volumes.

[hamdani yusuf (OP)]

Temperature is an extremely difficult thing to define.   It's a macroscopic property not a microscopic property.   As such temperature and most of thermodynamics only applies to large scales and average actions of particles in large bodies.

If we want to be pedantic, many other physical parameters are also hard to define, such as pressure and electric current. Even fundamental parameters such as mass, length, and time are also hard to define.
But we can continue using current definitions, even some obsolete ones, if they are useful.

[Bored chemist]

Given that all the molecules in a crystal are moving, how long does it take before you know if it has melted?

If there is energy flow, then after an hour or so I should be able to see some water in the left side of the container, which is previously filled with ice. Some ice would be formed in the right side.
If there is no energy flow, then after a day I should only still find ice in the left side of the container. The right side should still contain water.

If it takes an hour to notice any melting, but the fluctuations only last a nanosecond, will you notice any melting due to the fluctuations?

What I really can't understand is how you didn't realise that this was important.