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When discussing the conceptual issues of quantum mechanics, concepts like Bell's inequality, non-locality, and the Kochen-Specker theorem are often brought up. Many physicists have dedicated time to understanding how to interpret these theorems and what they imply on the limitation of what we can know about reality.

However, I've noticed that much less attention has been given to exploring the connection between the foundation of quantum theory and the laws of thermodynamics, especially the second and third laws.

Both theories impose strict limitations on what can be done and observed in our "reality," yet I haven't come across much work attempting to reconcile the two or utilize ideas from one theory in the other. While it's true that the development of these theories occurred in distinct contexts (microscopic physics and light-matter interactions for quantum mechanics, macroscopic bodies and many-body systems for thermodynamics), similar to the relationship between quantum mechanics and general relativity, there might be a physical level/scale in which the two theory might encounter and be incompatible, or partially compatible, or maybe even one can sustain the other. I’m particularly thinking of the the so-called measurement problem in quantum mechanics: a quantum theory expressed in the language of thermodynamics could naturally translate the second and third laws into the quantum realm and explain and constraint the non-linear axiom of quantum theory, i.e. the measurement update rule. Of course, all this makes sense unless one views these two theories as merely effective theories.

Are there any references available that address the problem of reconciling quantum mechanics with thermodynamics in the terms I have posed here? I believe this question is crucial for understanding the foundation of quantum mechanics and addressing the measurement problem. Perhaps a quantum theory expressed in the language of thermodynamics could naturally incorporate the second and third laws, leading to a resolution of this issue. Furthermore, this line of inquiry holds significance for practical applications such as quantum computing and other scalable systems that approach the thermodynamic limit.

Another question, more related to the foundation of quantum mechanics, is whether any work has been done on connecting quantum thermodynamics more directly with notion of non-locality, i.e. Bell scenario, Bell's inequalities or contextual inequalities.

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  • $\begingroup$ found this by searching scirp.org/journal/paperinformation.aspx?paperid=89142 $\endgroup$
    – anna v
    Jul 2, 2023 at 10:51
  • $\begingroup$ There are highly cited reviews on this topic so it is certainly not disregarded scholar.google.ca/… ... lots of results pop up when searching "quantum second law of thermodynamics" etc, so you may need to narrow your question a bit further $\endgroup$ Jul 2, 2023 at 13:30
  • $\begingroup$ @QuantumMechanic I tried to narrow a bit the question $\endgroup$ Jul 6, 2023 at 9:50

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Quantum Mechanics is the most fundamental theory we have about the universe (actually it's Quantum Field Theory, but let's ignore that distinction for the moment.) There is no other theory below it from which you can derive the Laws of Quantum Mechanics.

Thermodynamics is not a fundamental theory. Thermodynamics is useful when you want to consider a system that is too complex for you to individually describe the behavior of all its constituents. In principle, there is nothing stopping you from measuring the movement of all individual molecules in a glass of water and thereby obtaining a complete description of the system. But it's just not practical. Instead, you start to introduce concepts like temperature, which is simply the mean kinetic energy of all the individual particles.

Thus, the Laws of Thermodynamics are not fundamental. You can derive them by taking the laws of the underlying theory (i.e. classical mechanics in a classical system or quantum mechanics in a quantum system) and averaging over certain degrees of freedom you don't actually care about.

So at least on the theory side, there cannot be any conflicts between Quantum Mechanics and Thermodynamics, because one is derived from the other.

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  • $\begingroup$ You wrote "In principle, there is nothing stopping you from measuring the movement of all individual molecules in a glass of water and thereby obtaining a complete description of the system." How would you that measurement, in principle? $\endgroup$
    – hyportnex
    Jul 2, 2023 at 22:11
  • $\begingroup$ @hyportnex exactly! The issue I see in the standard formalism of quantum mechanics is exactly this ambiguity in the definition of measurement. It is just a postulate, but it doesn't really set the physical limitations that allow us to measure certain systems. It gives us a procedure, but how much are thes physically feasible, how much "resource" do we need? We don't really have the capabilities (technological) of measuring any observables, but this constraint does not come from the postulate itself. My question was: can thermodynamics help us on that issue? $\endgroup$ Jul 6, 2023 at 9:55
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Quantum mechanical equations of motion, such as the Schrodinger equation or equations of motion in quantum field theory, don't imply the collapse of the wavefunction. There are variants of quantum theory that modify the equations of motion to produce collapse:

https://arxiv.org/abs/1204.4325

The full implications of those modifications haven't been worked out. In addition, decoherence effects explain why classical equations of motion are a good approximation on the scale of everyday life:

https://arxiv.org/abs/1111.2189

and there are problems with trying to modify quantum theory:

https://arxiv.org/abs/2205.00568

Quantum theory can be applied to understanding statistical mechanics and thermodynamics and there is an enormous literature on this topic:

https://arxiv.org/abs/1907.01596

https://arxiv.org/abs/2104.11223

https://iopscience.iop.org/article/10.1088/1367-2630/18/6/063013/pdf

Interactions that copy information from one quantum system to another lead to each system having a mixed state. Such states don't allow interference and they have a higher entropy, so decoherence and entropy increase have a common origin.

As for the Bell correlations, there is an account of how those correlations arise as a result of locally inaccessible quantum information being carried in decoherent channels:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

This is entirely a result of information spreading by local interactions between quantum systems. Talk of quantum non-locality has not been backed up with any explanation of the alleged non-local mechanism to produce Bell correlations.

If you want to understand quantum theory and its implications you can only really do that by taking it seriously as an account of how the world works and working out its implications, including its implications for thermodynamics. Conversely, if you want to understand thermodynamics you have to look at how it is understood in the light of quantum theory instead of assuming quantum mechanical equations of motion are wrong without any clear reason.

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