▁A ▁therm od ynam ical ▁approach ▁to ▁the ▁high ▁energy ▁coll isions ▁first ▁proposed ▁by ▁E . ▁F erm i . ▁ ▁Part ition ▁function ▁The ▁partition ▁function ▁of ▁the ▁fire ball s ▁can ▁be ▁written ▁in ▁two ▁forms , ▁one ▁in ▁terms ▁of ▁its ▁density ▁of ▁states , ▁, ▁and ▁the ▁other ▁in ▁terms ▁of ▁its ▁mass ▁spectrum , ▁. ▁ ▁The ▁self - cons ist ency ▁principle ▁says ▁that ▁both ▁forms ▁must ▁be ▁asympt ot ically ▁equivalent ▁for ▁energ ies ▁or ▁masses ▁sufficiently ▁high ▁( as ym pt otic ▁limit ). ▁Also , ▁the ▁density ▁of ▁states ▁and ▁the ▁mass ▁spectrum ▁must ▁be ▁asympt ot ically ▁equivalent ▁in ▁the ▁sense ▁of ▁the ▁weak ▁constraint ▁proposed ▁by ▁H aged orn ▁as ▁ ▁. ▁ ▁These ▁two ▁conditions ▁are ▁known ▁as ▁the ▁self - cons ist ency ▁principle ▁or ▁bootstrap - idea . ▁After ▁a ▁long ▁mathematical ▁analysis ▁H aged orn ▁was ▁able ▁to ▁prove ▁that ▁there ▁is ▁in ▁fact ▁ ▁and ▁▁ ▁satisfying ▁the ▁above ▁conditions , ▁resulting ▁in ▁ ▁and ▁ ▁with ▁ ▁and ▁ ▁related ▁by ▁ ▁. ▁ ▁Then ▁the ▁asympt otic ▁partition ▁function ▁is ▁given ▁by ▁ ▁where ▁a ▁singular ity ▁is ▁clearly ▁observed ▁for ▁ ▁→ . ▁This ▁singular ity ▁determ ines ▁the ▁limit ing ▁temperature ▁ ▁in ▁H aged orn ' s ▁theory , ▁which ▁is ▁also ▁known ▁as ▁H aged orn ▁temperature . ▁ ▁H aged orn ▁was ▁able ▁not ▁only ▁to ▁give ▁a ▁simple ▁explanation ▁for ▁the ▁therm od ynam ical ▁aspect ▁of ▁high