Negative temperatures

Table of contents _ Some years ago I've published a post where I've briefly talked about the possibility to reach temperatures less than zero Kelvin. I've decided to republish it and extend the explanation with a physical example. Why we cannot reach the absolute zero When we talk about negative temperatures it's important to specify the scale: while negative values on the Celsius or Fahrenheit scales can be easily reached, it's impossible for a system to exist at zero Kelvin. There are several arguments that can be brought up to see why a system cannot exist at 0 K, those are reported below. The thermodynamic argument The well known third law of thermodynamics states that the entropy of a perfect crystal at the absolute zero is zero. We can see that such temperature cannot be reached if we consider the Nernst heat theorem, which states that as the temperatures approaches the absolute zero, the change in entropy of a transformation is negligible. $$ \lim_{T \to 0} \Delta S = 0 $$ This…