{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:33Z","timestamp":1740137253596,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","award":["2020R1F1A101075"],"award-info":[{"award-number":["2020R1F1A101075"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-023-03827-3","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T16:52:33Z","timestamp":1674147153000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Entropy production of quantum Markov semigroup associated with open quantum walks on the periodic graphs"],"prefix":"10.1007","volume":"22","author":[{"given":"Chul Ki","family":"Ko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0683-2898","authenticated-orcid":false,"given":"Hyun Jae","family":"Yoo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,19]]},"reference":[{"issue":"04n05","key":"3827_CR1","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1142\/S0217979204024070","volume":"18","author":"L Accardi","year":"2002","unstructured":"Accardi, L., Imafuku, K.: Dynamical detailed balance and local KMS condition for non-equilibrium states. Int. J. Mod. Phys. B 18(04n05), 435\u2013467 (2002)","journal-title":"Int. J. Mod. Phys. B"},{"issue":"5","key":"3827_CR2","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/BF01391504","volume":"258","author":"GS Agarwal","year":"1973","unstructured":"Agarwal, G.S.: Open quantum Markovian systems and the microreversibility. Z. Phys. 258(5), 409\u2013422 (1973)","journal-title":"Z. Phys."},{"key":"3827_CR3","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1142\/S0219025702001012","volume":"5","author":"S Albeverio","year":"2002","unstructured":"Albeverio, S., Goswami, D.: A remark on the structure of symmetric quantum dynamical semigroups. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5, 571\u2013579 (2002)","journal-title":"Infin. Dimens. Anal. Quantum Probab. Relat. Top."},{"key":"3827_CR4","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0034-4877(76)90046-X","volume":"10","author":"R Alicki","year":"1976","unstructured":"Alicki, R.: On the detailed balance condition for non-Hamiltonian systems. Rep. Math. Phys. 10, 249\u2013258 (1976)","journal-title":"Rep. Math. Phys."},{"issue":"2","key":"3827_CR5","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1142\/S0219025713500161","volume":"16","author":"JR Bola\u00f1os-Servin","year":"2013","unstructured":"Bola\u00f1os-Servin, J.R., Quezada, R.: A cycle decomposition and entropy production for circulant quantum Markov semigroups. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16(2), 23 (2013)","journal-title":"Infin. Dimens. Anal. Quantum Probab. Relat. Top."},{"key":"3827_CR6","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1006\/jfan.1996.3063","volume":"147","author":"F Cipriani","year":"1997","unstructured":"Cipriani, F.: Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras. J. Funct. Anal. 147, 259\u2013300 (1997)","journal-title":"J. Funct. Anal."},{"key":"3827_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.22199\/S07160917.1999.0003.00002","volume":"18","author":"F Fagnola","year":"1999","unstructured":"Fagnola, F.: Quantum Markov semigroups and quantum flows. Proyecciones 18, 1\u2013144 (1999)","journal-title":"Proyecciones"},{"doi-asserted-by":"crossref","unstructured":"Fagnola, F., Rebolledo, R.: From classical to quantum entropy production. In: Quantum Probability and Infinite Dimensional Analysis, QP\u2013PQ: Quantum Probability and White Noise Analysis, vol. 25, pp. 245\u2013261. World Scientific, Singapore (2010)","key":"3827_CR8","DOI":"10.1142\/9789814295437_0017"},{"key":"3827_CR9","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1007\/s00220-015-2320-1","volume":"335","author":"F Fagnola","year":"2015","unstructured":"Fagnola, F., Rebolledo, R.: Entropy production for quantum Markov semigroups. Commun. Math. Phys. 335, 547\u2013570 (2015)","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"3827_CR10","doi-asserted-by":"publisher","first-page":"1550013","DOI":"10.1142\/S1230161215500134","volume":"22","author":"F Fagnola","year":"2015","unstructured":"Fagnola, F., Rebolledo, R.: Entropy production and detailed balance for a class of quantum Markov semigroup. Open Syst. Inf. Dyn. 22(3), 1550013 (2015)","journal-title":"Open Syst. Inf. Dyn."},{"issue":"3","key":"3827_CR11","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1142\/S0219025707002762","volume":"10","author":"F Fagnola","year":"2007","unstructured":"Fagnola, F., Umanita, V.: Generators of detailed balance quantum Markov semigroups. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10(3), 335\u2013363 (2007)","journal-title":"Infin. Dimens. Anal. Quantum Probab. Relat. Top."},{"doi-asserted-by":"crossref","unstructured":"Fagnola, F., Umanita, V.: Detailed balance, time reversal and generators of quantum Markov semigroups. M. Zametki 84(1), 108-116 (2008) (Russian)","key":"#cr-split#-3827_CR12.1","DOI":"10.4213\/mzm5193"},{"doi-asserted-by":"crossref","unstructured":"translation Math. Notes 84(1), 108-115 (2008)","key":"#cr-split#-3827_CR12.2","DOI":"10.1134\/S0001434608070092"},{"key":"3827_CR13","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s00220-010-1011-1","volume":"298","author":"F Fagnola","year":"2010","unstructured":"Fagnola, F., Umanita, V.: Generators of KMS symmetric Markov semigroups on $${\\cal{B}}(h)$$ symmetry and quantum detailed balance. Commun. Math. Phys. 298, 523\u2013547 (2010)","journal-title":"Commun. Math. Phys."},{"key":"3827_CR14","series-title":"De Gruyter Stuidies in Mathematica","doi-asserted-by":"publisher","DOI":"10.1515\/9783110889741","volume-title":"Dirichlet Forms and Symmetric Markov Processes","author":"M Fukushima","year":"1994","unstructured":"Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes. De Gruyter Stuidies in Mathematica, vol. 19. De Gruyter, Berlin (1994)"},{"key":"3827_CR15","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1007\/BF02572383","volume":"219","author":"S Goldstein","year":"1995","unstructured":"Goldstein, S., Lindsay, J.M.: KMS symmetric semigroups. Math. Z. 219, 591\u2013608 (1995)","journal-title":"Math. Z."},{"key":"3827_CR16","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1063\/1.522979","volume":"17","author":"V Gorini","year":"1976","unstructured":"Gorini, V., Kossakowski, A., Surdarshan, E.C.G.: Completely positive dynamical semigroups of $$N$$-level systems. J. Math. Phys. 17, 821\u2013825 (1976)","journal-title":"J. Math. Phys."},{"key":"3827_CR17","doi-asserted-by":"publisher","first-page":"710","DOI":"10.1007\/s10955-019-02318-z","volume":"176","author":"CK Ko","year":"2019","unstructured":"Ko, C.K., Konno, N., Segawa, E., Yoo, H.J.: Central limit theorems for open quantum random walks on the crystal lattices. J. Stat. Phys. 176, 710\u2013735 (2019)","journal-title":"J. Stat. Phys."},{"key":"3827_CR18","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BF01625769","volume":"57","author":"A Kossakowski","year":"1977","unstructured":"Kossakowski, A., Frigerio, A., Gorini, V., Verri, M.: Quantum detailed balance and KMS condition. Commun. Math. Phys. 57, 97\u2013110 (1977)","journal-title":"Commun. Math. Phys."},{"key":"3827_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8542-4","volume-title":"Interacting Particle Systems","author":"TM Liggett","year":"1985","unstructured":"Liggett, T.M.: Interacting Particle Systems. Springer, Berlin (1985)"},{"key":"3827_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BF01608499","volume":"48","author":"G Lindblad","year":"1976","unstructured":"Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119\u2013130 (1976)","journal-title":"Commun. Math. Phys."},{"key":"3827_CR21","volume-title":"Introduction to the Theory of (Non-symmetric) Dirichlet Forms","author":"Z-M Ma","year":"1991","unstructured":"Ma, Z.-M., R\u00f6ckner, M.: Introduction to the Theory of (Non-symmetric) Dirichlet Forms. Springer, Berlin (1991)"},{"key":"3827_CR22","first-page":"931","volume":"95","author":"C Maes","year":"1995","unstructured":"Maes, C.: The fluctuation theorem as a Gibbs property. J. Stat. Phys. 95, 931 (1995)","journal-title":"J. Stat. Phys."},{"issue":"3","key":"3827_CR23","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1063\/1.533195","volume":"41","author":"C Maes","year":"2000","unstructured":"Maes, C., Redig, F., Van Moffaert, A.: On the definition of entropy production, via examples. J. Math. Phys. 41(3), 1528\u20131554 (2000)","journal-title":"J. Math. Phys."},{"key":"3827_CR24","first-page":"445","volume":"14","author":"C Maes","year":"2008","unstructured":"Maes, C., Netocn\u00fd, K., Wynants, B.: On and beyond entropy production: the case of Markov jump processes. Markov Process. Relat. Fields 14, 445\u2013464 (2008)","journal-title":"Markov Process. Relat. Fields"},{"key":"3827_CR25","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1063\/1.526164","volume":"25","author":"WA Majewski","year":"1984","unstructured":"Majewski, W.A.: The detailed balance condition in quantum statistical mechanics. J. Math. Phys. 25, 614\u2013616 (1984)","journal-title":"J. Math. Phys."},{"key":"3827_CR26","doi-asserted-by":"publisher","first-page":"7981","DOI":"10.1088\/0305-4470\/31\/39\/013","volume":"31","author":"WA Majewski","year":"1998","unstructured":"Majewski, W.A., Streater, R.F.: Detailed balance and quantum dynamical maps. J. Phys. A Math. Gen. 31, 7981\u20137995 (1998)","journal-title":"J. Phys. A Math. Gen."},{"key":"3827_CR27","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1142\/S0219025705001925","volume":"8","author":"YM Park","year":"2005","unstructured":"Park, Y.M.: Remarks on the structure of Dirichlet forms on standard forms of von Neumann algebras. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, 179\u2013197 (2005)","journal-title":"Infin. Dimens. Anal. Quantum Probab. Relat. Top."},{"key":"3827_CR28","series-title":"Monographs in Mathematics 85","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8641-3","volume-title":"An Introduction to Quantum Stochastic Calculus","author":"KR Parthasarathy","year":"1992","unstructured":"Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Monographs in Mathematics 85, Birkh\u00e4user, Basel (1992)"},{"key":"3827_CR29","series-title":"Surveys and Tutorials in Applied Mathematical Sciences","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-54177-6","volume-title":"Topological Crystallography with a View Towards Discrete Geometric Analysis","author":"T Sunada","year":"2013","unstructured":"Sunada, T.: Topological Crystallography with a View Towards Discrete Geometric Analysis. Surveys and Tutorials in Applied Mathematical Sciences, vol. 6. Springer, Berlin (2013)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03827-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-023-03827-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03827-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T22:01:09Z","timestamp":1676498469000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-023-03827-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,19]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["3827"],"URL":"https:\/\/doi.org\/10.1007\/s11128-023-03827-3","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2023,1,19]]},"assertion":[{"value":"26 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"81"}}