Interpretation of 2nd law of thermodynamics and observation in quantum mechanics

Question

The fundamental lesson of quantum mechanics has been that an observation "disturbs" the system under analysis as exemplified in Schrodinger's cat thought experiment or wave-function collapse interpretation of quantum mechanics.

The 2nd law of thermodynaimcs states that a system undergoing change, "changes" in a way that change in entropy is always greater than equal to 0.

My question is whether this lesson from quantum mechanics which deals with microscopic properties is responsible for the 2nd law of thermodynamics which deals with macroscopic phenomeon in general? In addition to that a supplemetary question is whether undertainty principle puts a lower bound on change in entropy of the system and surrounding?

Please point to the relevant literature if this has been in this light before.

Answer 1

Yes a possible connection between entropy and measurement has been explored for a long time. Overall, the results remain inconclusive because measurement in quantum mechanics remains a subtle issue and it is not fully agreed what is the best way to interpret what goes on.

First I should correct slightly your statement about entropy. The second law statement is not that the entropy of any system can never go down, it is that the entropy of an isolated system cannot go down. So when a system is not isolated, for example because it interacts with another system such as a microscope, then in principle its entropy could go up or down, depending on whether there is any exchange of entropy between the two systems.

Having said that, the kinds of physical process that are involved in recording measurement outcomes are the kinds that are indeed irreversible from a thermodynamic point of view. That is, they involve a net increase in the entropy of an isolated system. An example could be the sequence of sparks or current impulses generated in a particle detector, or the chemical process whereby spots are registered on photographic film, or the chemistry in the retina of an eye, and things like that. So it is reasonable to say that there is a connection between thermodynamic irreversibility and measurement of quantum states.

But the difficulty is that quantum theory itself can in principle be applied to describe the kinds of complex avalanche-like processes we are discussing, and quantum theory proposes that everything follows Schrodinger's equation, which amounts to saying that everything is reversible in principle. So this is, roughly, where the subject lies. Some people think Schrodinger's equation 'rules' and there is no real irreversibility, just a technological difficulty in controlling complex processes. Other people think Schrodinger's equation is not ruling in that way, but rather showing how the various parts of an overall irreversible process combine, leading to the probabilities for the available outcomes.

Answer 2

I do not think there is a direct relationship between the quantum mechanics evolution of physical systems at their atomic or sub-atomic level and the second principle of thermodynamics. The reason is that we know that it is possible to work with systems controlled by the laws of classical mechanics and still find the irreversible behavior at the basis of the second principle. For example, the quantum behavior of the atoms is irrelevant to explain the thermodynamic behavior of a colloidal suspension.

About the question of whether the uncertainty principle puts a lower bound on change in entropy of the system and surrounding, yes, quantum mechanics establishes a lower limit to entropy changes. The reason is that one cannot go below the change of entropy corresponding to a unitary variation in the number of microscopic states. However, what really matters is the ratio between the variation in the number of states and the number of states. For a thermodynamic system, the latter is a huge number, thus continuous changes are an excellent approximation.