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Recently I read an interesting article about negative temperature. I was puzzled because I thought before that temperature has definite meaning in thermodynamics: it tells about how fast atoms jiggle. Now if temperature can be negative, this means temperature has wider meaning...

I wonder if there is any deep physical meaning of temperature, not mathematical one.

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The negative temperature question is essentially a duplicate of physics.stackexchange.com/q/21851/2451 and links therein. –  Qmechanic Nov 10 '12 at 11:50
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The thermodynamic definition of temperature is

$$T \equiv \left( \frac{\partial S}{\partial U}\right)^{-1} $$

where $S$ is the thermodynamic entropy of the system and $U$ its internal energy. The thermodynamic concept of temperature $T$ is more general than the kinetic temperature $T_\mathrm{kin}$ (which only measures the average speed of molecules) because molecules do more than just translate in space.

A negative temperature simply means that the entropy of the system decreases $\delta S < 0$ when you add more energy $\delta U > 0$.

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Negative temperatures can only occur in systems where the energy spectrum is bounded above.The systems with Negative-temperature have the opposite characteristics. Adding energy reduces their disorder. But they are not cold in the conventional sense that heat will flow into them from the systems at (+)ve temperatures. In fact, systems with (-)ve absolute temperatures contain more atoms in high-energy states than is possible even at the hottest positive temperatures, so heat should always flow from them to systems above 0K.

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