<P> Another theory of absolute hot is based on the Hagedorn temperature, where the thermal energies of the particles exceed the mass - energy of a hadron particle - antiparticle pair . Instead of temperature rising, at the Hagedorn temperature more and heavier particles are produced by pair production, thus preventing effective further heating, given that only hadrons are produced . However, further heating is possible (with pressure) if the matter undergoes a phase change into a quark--gluon plasma . Therefore, this temperature is more akin to a boiling point rather than an insurmountable barrier . For hadrons, the Hagedorn temperature is 2 × 10 K, which has been reached and exceeded in LHC and RHIC experiments . However, in string theory, a separate Hagedorn temperature can be defined, where strings similarly provide the extra degrees of freedom . However, it is so high (10 K) that no current or foreseeable experiment can reach it . </P> <P> Considering only certain degrees of freedom in matter, such as nuclear spins, systems with a negative temperature can be produced . They occur because equipartitioning is too slow to allow communication between the degrees of freedom where thermal energy is stored, such as the vibrational, rotational and nuclear spin states of molecules . These systems are familiar from e.g. lasers . For these, theory predicts a mathematical singularity in temperature . When a spin system is excited with electromagnetic radiation and undergoes population inversion into an excited state, quantum physics formally assumes that its temperature function goes through a singularity . The spin temperature tends to positive infinity, before discontinuously switching to negative infinity . However, this applies only to specific degrees of freedom (the spin temperature in this case) in the system, while others would have normal temperature dependency . Thus, this singularity cannot be observed as ordinary sensible heat . If equipartitioning is possible, the system undergoes relaxation into a thermally uniform state with release of a finite quantity of heat . Before a physical infinite temperature could be reached, realistic ordinary matter would undergo phase transitions, such as evaporation, and never actually reach the infinite temperature . </P>

Is there a limit to how hot something can be