This is analogous to how all systems with positive absolute temperature preferentially occupy the lower energy states. The extra energy added past this point makes the previously symmetric distribution biased towards the higher energy states. These facts can be reconciled with how systems at negative temperatures have greater internal energy than at maximum entropy. It says that the probability of the system being in a particular energy state is proportional to negative exponential of the energy of the state divided by the Boltzmann constant (K) and the temperature. The probability that a system is in a particular energy state is given by something called the Boltzmann factor. We can understand negative absolute temperatures more meaningfully by thinking about how they affect the distribution of energy states the system has.

In order to have more internal energy than this we would require it to be greater than infinity which obviously is absurd. If this condition was not met then maximum entropy would occur at infinite internal energy. It now should also be clear why a system must have both upper and lower bounds on its allowed energy states to reach negative absolute temperature. If we increase the internal energy at a temperature of positive infinity it jumps directly to negative kelvins, skipping absolute zero. This shows why the existence of such temperatures does not violate the third law of thermodynamics. Notice thatĪ system has an absolute negative temperature when it contains more internal energy than at the point where maximum entropy is obtained (at a temperature of infinity or negative infinity). Since dS=0 at the maximum, it occurs only at temperatures of infinity or negative infinity.

This will become important later because it is a necessary condition a system must satisfy to have negative absolute temperature. Systems with both upper and lower bounds on the allowed energies, conversely, have a maximum entropy that they can obtain. If an infinite number of energy states are allowed, then the system’s entropy can increase without restraint. However, most systems do not have an upper bound on the allowed energy states, only a lower bound. Maximum entropy is achieved in the extreme case where the system is equally likely to be in every energy state that it is allowed to occupy. This makes sense because a system which has more energy will be more likely to occupy high energy states, resulting in a larger number of possible microscopic states and hence more disorder. Increasing the internal energy of a system usually increases its entropy (for positive temperatures). However, a system has a negative temperature by definition when increasing the internal energy causes the entropy to go down.Įntropy measures disorder, the number of possible microscopic arrangements which would produce the macroscopically observed properties. Thus when the entropy increases with the internal energy (at constant N and V) the temperature is positive.

What is the entropy at absolute zero