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I have checked the relevant questions on negative temperature and though they are very informative I did not satisfactorily get an answer to my question.

I simply want to know how can entropy decrease in a system?

So, either negative temperatures can never be achieved in isolated systems and therefore there is no violation, or is there something else going on here?

P.S.: I know the statistical definition of temperature and how it allows negative I also know the exact statement of 2nd law

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    $\begingroup$ The question is unclear. Just cool your system, entropy will go down $\endgroup$
    – Pavlo. B.
    Commented Apr 16, 2021 at 6:48

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So, either negative temperatures can never be achieved in isolated systems and therefore there is no violation, or is there something else going on here?

It is the word "isolated" that makes the difference. Entropy is decreasing when a diamond is formed, or any crystal out of the solution, but the system to be considered for the second law is the total solution, "crystal + solution it is in".

All living things live by continually decreasing their body's entropy and increasing the entropy of the surroundings.

Negative temperature achieved described here

Schneider and his colleagues reached such sub-absolute-zero temperatures with an ultracold quantum gas made up of potassium atoms. Using lasers and magnetic fields, they kept the individual atoms in a lattice arrangement. At positive temperatures, the atoms repel, making the configuration stable. The team then quickly adjusted the magnetic fields, causing the atoms to attract rather than repel each other. “This suddenly shifts the atoms from their most stable, lowest-energy state to the highest possible energy state, before they can react,”

all those magnets and lasers have to be taken into account for the entropy of the total system.

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  • $\begingroup$ So basically all systems that exhibit negative temperatures "necessarily" have to be non-isolated. Is that correct? $\endgroup$
    – Lost
    Commented Apr 16, 2021 at 6:57
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    $\begingroup$ @Lost yes, the whole system has to be considere dor the second law, and negative temperature can only be achieved with a lot of intsturmentation to induce it. $\endgroup$
    – anna v
    Commented Apr 16, 2021 at 7:44
  • $\begingroup$ Could you also answer my other question in statistical mechanics? I have written the question and I really am confused in that but nobody seems to answer. $\endgroup$
    – Lost
    Commented Apr 16, 2021 at 9:09
  • $\begingroup$ physics.stackexchange.com/posts/comments/1415935?noredirect=1 $\endgroup$
    – Lost
    Commented Apr 16, 2021 at 9:10

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