?url_ver=Z39.88-2004&rft_id=arXiv%3A1710.11422&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F4033%2F&rft.title=Reconnecting+statistical+physics+and+combinatorics+beyond+ensemble+equivalence&rft.creator=Squartini%2C+Tiziano&rft.creator=Garlaschelli%2C+Diego&rft.subject=HA+Statistics&rft.subject=QC+Physics&rft.description=In+statistical+physics%2C+the+challenging+combinatorial+enumeration+of+the+configurations+of+a+system+subject+to+hard+constraints+(microcanonical+ensemble)+is+mapped+to+a+mathematically+easier+calculation+where+the+constraints+are+softened+(canonical+ensemble).+However%2C+the+mapping+is+exact+only+when+the+size+of+the+system+is+infinite+and+if+the+property+of+ensemble+equivalence+(EE)%2C+i.e.+the+asymptotic+identity+of+canonical+and+microcanonical+large+deviations%2C+holds.+For+finite+systems%2C+or+when+EE+breaks+down%2C+statistical+physics+is+currently+believed+to+provide+no+answer+to+the+combinatorial+problem.+In+contrast+with+this+expectation%2C+here+we+establish+exact+relationships+connecting+conjugate+ensembles+in+full+generality%2C+even+for+finite+system+size+and+when+EE+does+not+hold.+We+also+show+that+in+the+thermodynamic+limit+the+ensembles+are+directly+related+through+the+matrix+of+canonical+(co)variances+of+the+constraints%2C+plus+a+correction+term+that+survives+only+if+this+matrix+has+an+infinite+number+of+finite+eigenvalues.+These+new+relationships+restore+the+possibility+of+enumerating+microcanonical+configurations+via+canonical+probabilities%2C+thus+reconnecting+statistical+physics+and+combinatorics+in+realms+where+they+were+believed+to+be+no+longer+in+mutual+correspondence.&rft.publisher=arXiv&rft.date=2017&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F4033%2F1%2F1710.11422.pdf&rft.identifier=++Squartini%2C+Tiziano+and+Garlaschelli%2C+Diego++Reconnecting+statistical+physics+and+combinatorics+beyond+ensemble+equivalence.++Working+Paper+++arXiv+++++++++&rft.relation=https%3A%2F%2Farxiv.org%2Fpdf%2F1710.11422&rft.relation=arXiv%3A1710.11422