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Second Law of Thermodynamics

From the second law of thermodynamics, the entropy of the universe must always increase. However, most explanations of entropy state that it is the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system. Hence it is favourable for things to move to a state of disorder.

Consider a hot object coming into contact with a cold one. By reaching a temperature equilibrium, this it the state where entropy is maximum, and most statistically likely. However, although very unlikely, couldn't the temperature of the hot object actually increase, therefore decreasing entropy. I understand that this is almost impossible, however the probability is non zero.

So when we restate the entropy of the universe as always increasing, can there be situations where the entropy actually decreases although unlikely?

Something must be wrong with my intuition as stated above. What is wrong?

Quin Gardiner Bax
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    "So when we restate the entropy of the universe as always increasing" --no serious source should do this. To start with, it is hard to define the entropy of the universe. If you want my two cents: Read the work of Jaynes to gain a solid understanding of the second law, entropy and statistical mechanics in general. A good intro textbook, which however works with QM, is by Jochen Rau. The books by R. Balian are also very nice. – Tobias Fünke Jan 23 '24 at 09:07
  • Sure entropy can fluctuate on small scales as per uncertainty principle $\Delta T \Delta S \Delta t \geq \hbar/2$. – Agnius Vasiliauskas Jan 23 '24 at 09:42

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