{"paper":{"title":"Entropic Fluctuations in Quantum Statistical Mechanics: A Review","arxiv_id":"2610.40463","primary_cat":"math-ph","submitted_at":"2026-10-29T17:05:03+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The celebrated Evans--Searles, respectively Gallavotti--Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.98,"id":"s1","own":true,"role":"contribution","text":"In this paper, we review and compare several possible extensions of these fluctuation theorems to quantum systems.","hedge":{"p":0.83,"label":"asserted"},"own_p":0.52,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.19,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":2,"p":0.94,"id":"s2","own":true,"role":"contribution","text":"We present, in an introductory way, the approach proposed in a recent series of works [Lett. Math.","hedge":{"p":0.82,"label":"asserted"},"own_p":0.6,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.94,"interpretation":0.0}},{"i":3,"p":0.57,"id":"s3","own":false,"role":"contribution","text":"Phys. 114, 32 (2024): doi:10.1007/s11005-024-01777-0], [Rev. Math.","hedge":{"p":0.92,"label":"unclear"},"own_p":0.06,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.67,"role_probabilities":{"gap":0.01,"method":0.03,"result":0.0,"background":0.39,"limitation":0.0,"future_work":0.0,"contribution":0.57,"interpretation":0.0}},{"i":4,"p":0.54,"id":"s4","own":false,"role":"background","text":"Phys 38, 2461006 (2026): doi:10.1142/S0129055X24610063], [Commun. Math.","hedge":{"p":0.96,"label":"unclear"},"own_p":0.05,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.01,"method":0.02,"result":0.0,"background":0.54,"limitation":0.0,"future_work":0.0,"contribution":0.43,"interpretation":0.0}},{"i":5,"p":0.53,"id":"s5","own":false,"role":"background","text":"Phys. 406, 201 (2025): 10.1007/s00220-025-05360-z] and [J. Math.","hedge":{"p":0.9,"label":"unclear"},"own_p":0.07,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.58,"role_probabilities":{"gap":0.02,"method":0.04,"result":0.0,"background":0.53,"limitation":0.0,"future_work":0.0,"contribution":0.41,"interpretation":0.0}},{"i":6,"p":0.82,"id":"s6","own":true,"role":"contribution","text":"Phys. 67, 022101 (2026): doi:10.1063/5.0311182] including a previously missing extension of the Gallavotti--Cohen (steady state) version of the FT to two-time measurement entropy production in the algebraic setting of quantum dynamical systems.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.79,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.3,"role_probabilities":{"gap":0.17,"method":0.0,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.82,"interpretation":0.0}},{"i":7,"p":0.62,"id":"s7","own":false,"role":"contribution","text":"We focus on the open quantum systems, where a small system interacts with several (infinitely extended) reservoirs, and discuss the following approaches: naive, two-time measurement, phase space contraction and ancilla state tomography.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.48,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.21,"role_probabilities":{"gap":0.0,"method":0.33,"result":0.0,"background":0.03,"limitation":0.02,"future_work":0.0,"contribution":0.62,"interpretation":0.0}},{"i":8,"p":0.72,"id":"s8","own":false,"role":"contribution","text":"We review the connection with modular theory.","hedge":{"p":0.87,"label":"asserted"},"own_p":0.33,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.19,"result":0.0,"background":0.09,"limitation":0.0,"future_work":0.0,"contribution":0.72,"interpretation":0.0}},{"i":9,"p":0.5,"id":"s9","own":false,"role":"background","text":"The latter provides a way to extend the classical notions to the quantum domain.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.09,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.35,"result":0.0,"background":0.5,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.1}},{"i":10,"p":0.88,"id":"s10","own":false,"role":"contribution","text":"We discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in [Nonlinearity 24, 699 (2011): doi:10.1088/0951-7715/24/3/003].","hedge":{"p":0.88,"label":"asserted"},"own_p":0.25,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.12,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":11,"p":0.74,"id":"s11","own":true,"role":"contribution","text":"Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators and apply this approach to a paradigmatic model of non-equilibrium statistical mechanics: the spin-fermion model.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.23,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.23,"result":0.03,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.74,"interpretation":0.0}},{"i":12,"p":0.99,"id":"s12","own":true,"role":"interpretation","text":"The results presented here shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.66,"main_claim_p":0.55,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.99}}]},"compiled":{"main_claim":{"p":0.99,"text":"The results presented here shed a new light on the nature of entropic fluctuations in quantum 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