How you interpret is that it's pop science misinterpretation. Temperature is necessarily defined for systems in equilibrium. Systems with "negative T" aren't in equilibrium hence T isn't strictly defined.
So, what do we mean by neg T? Solutions to Boltzmann's distribution for population inversion (more electrons, say, in an excited state than the ground state).
Usually, the hotter something is, the more excited states are occupied; but in equilibrium there are always more occupied ground states.
So "hotter than any positive T" refers to "negative T"s having more excited states than positive T
I used to live in Rome in the late 90s. As many as tourists as there were, and there were many, the volume must have doubled in twenty years.
Last time I visited, I felt an overwhelming anxiety that Rome didn't exist anymore. Instead I was walking through an amusement park shaped like it.
Friends I spoke to, who live in the Alban Hills, told me they'd stopped going to Rome 10 years earlier. Which is insane because she can trace her family in Rome proper to the 16th century.
How you interpret is that it's pop science misinterpretation. Temperature is necessarily defined for systems in equilibrium. Systems with "negative T" aren't in equilibrium hence T isn't strictly defined.
So, what do we mean by neg T? Solutions to Boltzmann's distribution for population inversion (more electrons, say, in an excited state than the ground state).
Usually, the hotter something is, the more excited states are occupied; but in equilibrium there are always more occupied ground states.
So "hotter than any positive T" refers to "negative T"s having more excited states than positive T