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The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve toward thermodynamic equilibrium—the state of maximum entropy.

So imagine a box where there are lot of atoms with different temperatures, they will start to move and the temperature will start to come to a number k. Similarly entropy will start to increase to a number x, and it wouldn't increase after it reaches the maximum entropy. What I ask is will atoms in those boxes stop moving if entropy reaches the maximum since the system couldn't get more disordered?

Thank you.

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  • $\begingroup$ The second law implies that "the entropy of an isolated system never decreases", but it $does~not~state~it$. Such statement is trivial, since entropy of isolated system is constant. The second law is more general than that. It has many formulations, one of which is "heat cannot spontaneously move from colder to warmer body". The statement "isolated systems spontaneously evolve toward thermodynamic equilibrium" was argued to be independent of 2nd law and was called the Minus First Law of thermodynamics. See philsci-archive.pitt.edu/313/1/engtot.pdf $\endgroup$ Commented Dec 30, 2013 at 15:27

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No - thermal equilibrium means no heat transfer (essentially when the temperature of the gas inside the box remains constant but not necessarily zero). The atoms will continue to move, vibrate, rotate, etc... but do so now at a constant temperature.

Also, just to be clear, an individual atom does not have a temperature - you need a large collection of atoms to define temperature. Nevertheless, the scenario you described could occur if you consider a box that had a different temperatures in different areas of the box.

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  • $\begingroup$ Yes that's what I mean $\endgroup$ Commented Dec 30, 2013 at 15:03
  • $\begingroup$ But if the atoms will continue to move vibrate, rotate... how could they if they reached the maximum level of disorder? $\endgroup$ Commented Dec 30, 2013 at 15:05
  • $\begingroup$ Because each individual atom is not necessarily moving at the same speed as the other atoms. That is, the movement is maximally random. Furthermore, when we say "maximum entropy" we mean maximum that is allowed for the system. In the example you gave, the temperature being zero could never occur because of energy conservation (where would all kinetic energy go of the previously moving atoms?). $\endgroup$
    – mcFreid
    Commented Dec 30, 2013 at 15:08
  • $\begingroup$ I understand now. $\endgroup$ Commented Dec 30, 2013 at 15:12

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