Can thermodynamics macrostates hide relevant quantum information ?

[mirko1]

I’m a chemistry student, I’ve been thinking about the connection between quantum mechanics and thermodynamics.
In thermodynamics we describe a system through macroscopic quantities such as T, P, Energy…
Quantum mechanics on the other hand, gives us more detailed description on the microscopic state.
This made me wonder what exactly is lost when we go from the quantum description to a thermodynamics macrostate.
In particular:
Suppose 2 quantum states are indistinguishable with respect to the macroscopic variables we use to define the thermodynamic state, but have different “microscopic correlations” or different “internal quantum structure”.
Could those differences still affect thermodynamic quantities such as extractable work, free energy or entropy production ?
Or does fixing the thermodynamic macro state necessarily make all the remaining microscopic information thermodynamically irrilevant?
I’m asking because I initially arrived at this idea by thinking of the wave function not only as a probability amplitude, but also as a possible description of the information and dynamics of the whole system.
Thanks for reading, I’m curious to hear what you think.

 

[jeffn1]

This may be a dumb question (if so, I apologize in advance), but have you looked into quantum thermodynamics?

 

[mirko1]

Yes I have, I recently started looking into quantum thermodynamics, especially the connection between quantum information, correlation and coarse-graining.
That’s what actually led me to this question. I’m trying to understand if some information contained in the full quantum state could be lost when we describe the system only through its thermodynamic macrostate.

 

[PeterDonis]

I recently started looking into quantum thermodynamics, especially the connection between quantum information, correlation and coarse-graining

What references have you looked at?

 

[PeterDonis]

I’m trying to understand if some information contained in the full quantum state could be lost when we describe the system only through its thermodynamic macrostate.

The answer to this is easy: "of course". The whole point of thermodynamics, and more generally of statistical mechanics, is to not try to work with information about the microstate because there's too much of it to usefully handle, and work instead with the coarse-grained information in the macrostate. Indeed, in contexts where we use thermodynamics, we don't even know what the microstate is to begin with; the thermodynamic variables in the macrostate are all that we actually know about the system.

This is not limited to QM, by the way; the same is true of classical statistical mechanics and thermodynamics based on underlying classical microstates.

 

[PeterDonis]

does fixing the thermodynamic macro state necessarily make all the remaining microscopic information thermodynamically irrilevant?

Yes. As per my previous post just now, that's the whole point of thermodynamics.

 

[mirko1]

I agree that in ordinary thermodynamic situations, most microscopic information can be safely discarded. What I’m wondering is whether there could be situations where the opposite becomes important:
where we normally go from the microscopic description to the macroscopic one, but under extreme, strongly interacting or far from equilibrium conditions we may need to go back to the microscopic description to understand the macroscopic.

Maybe there are regimes where the microscopic information that thermodynamics normally ignores becomes relevant again.

 

[PeterDonis]

I agree that in ordinary thermodynamic situations, most microscopic information can be safely discarded. W

It's not a matter of it being "discarded". We don't even have it in the first place. That's why we use thermodynamics--because we don't know any more information than what the thermodynamic variables tell us.'

under extreme, strongly interacting or far from equilibrium conditions we may need to go back to the microscopic description to understand the macroscopic.

If we have a microscopic description and can use it to make predictions, we don't need a macroscopic description. In such a situation we would not even be doing thermodynamics in the first place.

 

[mirko1]

I think I explained my point badly. I’m not saying that we should replace thermodynamics with a microscopic description whenever we can use one.
What I’m wondering is whether the macroscopic variables we use are always enough to predict how the system will evolve.
In other words, could two systems be indistinguishable with respect to the macroscopic variables we use, but still evolve differently because of microscopic information that was lost in the coarse-graining?
So my question is less about whether we need a microscopic description instead of thermodynamics, and more about when a particular coarse-grained description ceases to be dynamically sufficient.

-Rubino, Brukner & Manzano 2026, Coarse-grained quantum thermodynamics: observation-dependent quantities, observation-independent laws.
studies how losing microscopic information through coarse graining can affect quantities such as work and dissipation.
-Rignon-Bret & Elouard 2026, Qquantum stochastic thermodynamics of macroscopic systems: an algebric approach.
looks at macroscopic quantum thermodynamics and at nonequilibrium resources that can be hidden by coarse graining.
I’m still exploring the literature

 

[Matterwave]

Are you asking about the domain of validity of thermodynamics?

I still have a hard time parsing your question into a concrete one.

 

[PeterDonis]

What I’m wondering is whether the macroscopic variables we use are always enough to predict how the system will evolve.

They are never enough to predict with certainty how the system will evolve. How accurate the predictions we can make from them are will depend on the situation.

could two systems be indistinguishable with respect to the macroscopic variables we use, but still evolve differently because of microscopic information that was lost in the coarse-graining?

Of course. The question would be whether the difference would be something we could detect. Again, that would depend on the situation.

To give two simplified idealized examples:

Say we have two containers of gas, the same gas (say it's nitrogen, N2, to be concrete), same thermodynamic variables in both cases (volume, temperature, pressure, etc. all the same), and assumed to be in thermodynamic equilibrium with their environment. Obviously that does not mean the two containers are identical; they will in general be in different microstates, and they will evolve differently in terms of the microstate they are in. But they will remain indistinguishable as far as the thermodynamic variables are concerned, because we've specified that they are both in thermodynamic equilibrium and we're not doing anything to change that. (For example, we're not applying a heat source to one container but not the other.) We can make that prediction accurately, but it doesn't predict very much--it certainly doesn't give us any dynamics, since we're basically saying nothing more than that everything we can measure stays the same.

Now, for a contrasting example, say we have two containers, in each of which we have a partition: on one side of the partition there is N2 gas, on the other side is vacuum. The starting condition is the same in both cases--same volume, temperature, pressure, etc. of N2 gas, same empty volume on the other side of the partition. Now we remove both partitions and let both gases equilibrate. Thermodynamics allows us to predict the eventual equilibrium state (assuming we know the temperature of the environment), but not how long it will take for each container to reach it, or even that they will necessary take the same time to reach it. We might be able to measure differences in the details of how the temperature, pressure, etc. of the gas in each container changes with time as they equilibrate, and ultimately those differences would be due to differences in their exact microstate. (In practice it would be difficult to set such an experiment up so that we could actually detect such differences, but in principle it would be possible.) If we knew the exact microstate of each gas, we could predict the exact time evolution of each one--but if all we know is the thermodynamic variables, we can't.

Note, btw, that neither of these examples involve QM at all. I'm not sure there's anything specific to QM in the question you're asking; it looks to me like a general question about the limitations of statistical mechanics.

 

[mirko1]

Thank you for the answers!
And maybe a glass transition example is closer to what I was trying to describe.

Imagine two glass samples at exactly the same T, P and density. From the usual thermodynamic variables, they look identical.
However, suppose they were prepared differently: one was cooled quickly, while the other was cooled slowly and allowed to relax for longer. Their microscopic structures would not necessarily be the same.

Now we let them evolve under exactly the same conditions. Could they have different relaxation dynamics even though their macroscopic variables are initially identical?
If so, this is closer to what I mean by “information lost in coarse-graining becoming relevant”
the information is not needed to describe the state at that instant, but it may be needed to predict how that state will evolve.
I think this is the distinction I was struggling to express.

 

[PeterDonis]

Now we let them evolve under exactly the same conditions. Could they have different relaxation dynamics even though their macroscopic variables are initially identical?

I already answered this in the second example in post #11: since by construction their microstates are different, then in principle their exact time evolution can be different. Whether this difference would be detectable in practice is a different matter.

the information is not needed to describe the state at that instant

Yes, it is: the information in question is the microstate of the two objects at that instant, which, as you have specified, is different, and that difference is why their subsequent time evolutions can be different. If they were both in the exact same microstate at the same instant, they could not have different time evolutions.

 

[mirko1]

Are you asking about the domain of validity of thermodynamics?

I still have a hard time parsing your question into a concrete one.

I already answered this in the second example in post #11: since by construction their microstates are different, then in principle their exact time evolution can be different. Whether this difference would be detectable in practice is a different matter.


Yes, it is: the information in question is the microstate of the two objects at that instant, which, as you have specified, is different, and that difference is why their subsequent time evolutions can be different. If they were both in the exact same microstate at the same instant, they could not have different time evolutions.

Thanks, I really appreciate your answer! I think what I’m really interested in is the predictive side of this. If two microscopic states are indistinguishable under a given coarse-grained description, but later produce experimentally distinguishable macroscopic behaviour, then that description was not fully predictive for that dynamics. In that case, I’d like to understand what additional information or variables would be needed to make the model predictive again. That’s probably the part I’m most interested in exploring.

 

[PeterDonis]

In that case, I’d like to understand what additional information or variables would be needed to make the model predictive again.

You need the microstate. That's what the actual dynamics of the system depends on.

Take a look at the equations of thermodynamics. How many of them are dynamical?

 

[mirko1]

You need the microstate. That's what the actual dynamics of the system depends on.

Take a look at the equations of thermodynamics. How many of them are dynamical?

Maybe I was approaching the problem from the wrong side by focusing on thermodynamics.

What I’m really interested in is whether there can be useful intermediate descriptions between the full microstate and a macroscopic description, and under what conditions those reduced descriptions remain predictive of the dynamics.
So perhaps the area I should be looking into is nonequilibrium statistical mechanics and dynamical coarse-graining, rather than thermodynamics itself.
Thanks again

 

[Matterwave]

Thermodynamics might have indeed been a red herring. It seems your curiosity is more about "micro" vs "macro" descriptions or microphysical/dynamical vs phenomenological descriptions. Something along those lines?

Given where you've pivoted with your question, I wonder if Hysteresis is your interest: https://en.wikipedia.org/wiki/Hysteresis

 

[mirko1]

Thermodynamics might have indeed been a red herring. It seems your curiosity is more about "micro" vs "macro" descriptions or microphysical/dynamical vs phenomenological descriptions. Something along those lines?

Given where you've pivoted with your question, I wonder if Hysteresis is your interest: https://en.wikipedia.org/wiki/Hysteresis

Hysteresis is an interesting suggestion too, so I’ll definitely look into it. Thanks again for pointing me in that direction!