I Laws of thermodynamics and their application to quantum physics

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The Second Law of Thermodynamics states that the total entropy of an isolated system never decreases. But in a time-reversal experiment in quantum systems, would it be possible to observe an effective decrease in entropy? How does this reconcile with the classical view of irreversibility?
A Segunda Lei da Termodinâmica afirma que a entropia total de um sistema isolado nunca diminui. Mas em um experimento de reversão de tempo em sistemas quânticos, seria possível observar uma diminuição efetiva na entropia? Como isso se reconcilia com a visão clássica da irreversibilidade?
 
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Priscilaifrj said:
a time-reversal experiment
How would you run such an experiment?
 
And how exactly do you define quantum entropy of a closed system? (There are several inequivalent definitions, see e.g. Sec. 5.3 of my https://arxiv.org/abs/2308.10500)
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
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