Editing Negative temperature (section)

== Temperature and disorder ==
{{Unreferenced section|date=July 2024}}
The distribution of energy among the various [[translation (physics)|translational]], [[oscillation|vibrational]], [[rotation]]al, [[Electron configuration|electronic]], and [[atomic nucleus|nuclear]] modes of a system determines the macroscopic temperature. In a "normal" system, thermal energy is constantly being exchanged between the various modes.

However, in some situations, it is possible to isolate one or more of the modes. In practice, the isolated modes still exchange energy with the other modes, but the [[Speed|time scale]] of this exchange is much slower than for the exchanges within the isolated mode. One example is the case of [[atomic nucleus|nuclear]] [[Spin (physics)|spins]] in a strong external [[magnetic field]]. In this case, energy flows fairly rapidly among the spin states of interacting atoms, but energy transfer between the nuclear spins and other modes is relatively slow. Since the energy flow is predominantly within the spin system, it makes sense to think of a spin temperature that is distinct from the temperature associated to other modes.

A definition of [[Temperature#Second law of thermodynamics|temperature]] can be based on the relationship:

:<math>T = \frac{dq_\mathrm{rev}}{dS}</math>

The relationship suggests that a ''positive temperature'' corresponds to the condition where [[entropy]], {{mvar|S}}, increases as thermal energy, {{math|''q''<sub>rev</sub>}}, is added to the system. This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and non-spin-related electronic and nuclear modes. The reason for this is that there are an [[Infinity|infinite]] number of these types of modes, and adding more heat to the system increases the number of modes that are energetically accessible, and thus increases the entropy.