▁systems , ▁instead ▁of ▁taking ▁the ▁limit ▁of ▁finite ▁systems . ▁ ▁A ▁measure ▁is ▁a ▁Gib bs ▁measure ▁if ▁the ▁conditional ▁prob abilities ▁it ▁indu ces ▁on ▁each ▁finite ▁sub system ▁satisfy ▁a ▁consist ency ▁condition : ▁if ▁all ▁degrees ▁of ▁freedom ▁outside ▁the ▁finite ▁sub system ▁are ▁fro zen , ▁the ▁canonical ▁ensemble ▁for ▁the ▁sub system ▁subject ▁to ▁these ▁boundary ▁conditions ▁matches ▁the ▁prob abilities ▁in ▁the ▁Gib bs ▁measure ▁conditional ▁on ▁the ▁fro zen ▁degrees ▁of ▁freedom . ▁ ▁The ▁Hamm ers ley – Cl iff ord ▁theorem ▁implies ▁that ▁any ▁probability ▁measure ▁that ▁satisfies ▁a ▁Mark ov ▁property ▁is ▁a ▁Gib bs ▁measure ▁for ▁an ▁appropriate ▁choice ▁of ▁( loc ally ▁defined ) ▁energy ▁function . ▁Therefore , ▁the ▁Gib bs ▁measure ▁applies ▁to ▁w ides p read ▁problems ▁outside ▁of ▁physics , ▁such ▁as ▁Hop field ▁networks , ▁Mark ov ▁networks , ▁Mark ov ▁logic ▁networks , ▁and ▁bounded ▁rational ▁potential ▁games ▁in ▁game ▁theory ▁and ▁econom ics . ▁ ▁A ▁Gib bs ▁measure ▁in ▁a ▁system ▁with ▁local ▁( finite - range ) ▁interactions ▁maxim izes ▁the ▁entropy ▁density ▁for ▁a ▁given ▁expected ▁energy ▁density ; ▁or , ▁equival ently , ▁it ▁minim izes ▁the ▁free ▁energy ▁density . ▁ ▁The ▁Gib bs ▁measure ▁of ▁an ▁infinite ▁system ▁is ▁not ▁necessarily ▁unique , ▁in ▁contrast ▁to ▁the ▁canonical ▁ensemble ▁of ▁a ▁finite ▁system , ▁which ▁is ▁unique . ▁The ▁existence ▁of ▁more ▁than ▁one ▁Gib bs ▁measure ▁is ▁associated ▁with ▁statistical ▁phen omena ▁such ▁as ▁symmetry