How can energy change in thermal interaction without changing external parameters?

[Yathindra]

It was described that the thermal interaction changes average energy of each system by a different amount and the external parameters do not change at all in a thermal interaction. I do not understand how energy of a system changes without a change in external parameters.

 

[Chestermiller]

It was described that the thermal interaction changes average energy of each system by a different amount and the external parameters do not change at all in a thermal interaction. I do not understand how energy of a system changes without a change in external parameters.

Can you please provide more context or a direct quote regarding this?

 

[Yathindra]

Sure, the explanation in reif proceeds as follows:
The quantum energy levels of a system Er depend on external parameters like Volume, Magnetic field, etc. Er(x1,x2,x3...) In a purely thermal interaction ( only heat is exchanged and work done is zero), these external parameters are not altered. And yet we see a change in the overall energy of the system. But, this change is due to the relative number of systems of an ensemble being on those energy levels alters. Whereas in a mechanical interaction, external parameters do change and so Er which is a function of those would obviously change.
What confuses me is the idea of an ensemble here. It looks like in some cases even though a hotter and colder system is in contact, energy transfer would not take place.!

PFA. (page 66, chapter 2)

 

[Chestermiller]

If a hotter and a colder system are brought into contact, the distribution of energy levels within each of them changes as a result of the heat transferred from the hotter system to the colder system.

 

[haider]

If a hotter and a colder system are brought into contact, the distribution of energy levels within each of them changes as a result of the heat transferred from the hotter system to the colder system.

I'm going through Reif and had the same question. This is how I understand it:

When a system $A$ with mean energy $\bar{E}=\varepsilon$ interacts (only) thermally with a system $A^{'}$ by transfering heat $\Delta E = \varepsilon / 3$, the proportion of systems $A$ of the ensemble in various energy levels (of system $A$) changes such that the mean energy of a system $A$ in this ensemble is $\frac{2}{3}\varepsilon$, but the energy levels themselves are the same. Also there should be a similar shift in the proportions of systems $A^{'}$ over various energy levels (of $A^{'}$) such that the mean energy of an $A^{'}$ in the ensemble is $\frac{1}{3}\varepsilon$

On the other hand if these two systems interacted mechanically the energy levels of both systems would change as a result of a change in external paramaters. As I understand it , external parameters are those that appear in the Hamiltonian, which is the reason for the energy levels changing (different Hamiltonian $=$ different quantum system $\implies$ different energy eigenstates $=$ different energy levels. The proportion of systems should also shift accordingly to change the mean energies of the system in line with macroscopic thermodynamics.

Am I correct in understanding it this way?