▁divided ▁in ▁N ▁discrete ▁values ▁with ▁a ▁difference ▁between ▁them ▁of ▁, ▁such ▁that ▁ ▁. ▁ ▁Given ▁this ▁discrete ▁spectrum , ▁the ▁algorithm ▁is ▁initialized ▁by : ▁ ▁setting ▁all ▁entries ▁of ▁the ▁micro can on ical ▁entropy ▁to ▁zero , ▁ ▁initial izing ▁ ▁and ▁initial izing ▁the ▁system ▁randomly , ▁by ▁putting ▁in ▁a ▁random ▁configuration ▁. ▁ ▁The ▁algorithm ▁then ▁performs ▁a ▁mult ican on ical ▁ensemble ▁simulation : ▁a ▁Metropol is – H ast ings ▁random ▁walk ▁in ▁the ▁phase ▁space ▁of ▁the ▁system ▁with ▁a ▁probability ▁distribution ▁given ▁by ▁ ▁and ▁a ▁probability ▁of ▁propos ing ▁a ▁new ▁state ▁given ▁by ▁a ▁probability ▁distribution ▁. ▁A ▁hist ogram ▁ ▁of ▁visited ▁energ ies ▁is ▁stored . ▁Like ▁in ▁the ▁Metropol is – H ast ings ▁algorithm , ▁a ▁proposal - accept ance ▁step ▁is ▁performed , ▁and ▁consists ▁in ▁( see ▁Metropol is – H ast ings ▁algorithm ▁over view ): ▁▁ ▁propos ing ▁a ▁state ▁ ▁according ▁to ▁the ▁arbitrary ▁proposal ▁distribution ▁▁ ▁accept / ref use ▁the ▁proposed ▁state ▁according ▁to ▁ ▁where ▁ ▁and ▁. ▁ ▁After ▁each ▁proposal - accept ance ▁step , ▁the ▁system ▁trans its ▁to ▁some ▁value ▁, ▁ ▁is ▁increment ed ▁by ▁one ▁and ▁the ▁following ▁update ▁is ▁performed : ▁ ▁. ▁ ▁This ▁is ▁the ▁cru cial ▁step ▁of ▁the ▁algorithm , ▁and ▁it ▁is ▁what ▁makes ▁the ▁Wang ▁and ▁Land au ▁algorithm ▁non - Mark ov ian : ▁the ▁st ochastic ▁process ▁now ▁depends ▁on ▁the ▁history