{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T11:38:26Z","timestamp":1761824306835,"version":"build-2065373602"},"reference-count":75,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T00:00:00Z","timestamp":1617926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters\u2014i.e., the efficiency and work done\u2014is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.<\/jats:p>","DOI":"10.3390\/e23040439","type":"journal-article","created":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T10:05:21Z","timestamp":1617962721000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1160-3603","authenticated-orcid":false,"given":"Pritam","family":"Chattopadhyay","sequence":"first","affiliation":[{"name":"Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9436-8871","authenticated-orcid":false,"given":"Ayan","family":"Mitra","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5160-6032","authenticated-orcid":false,"given":"Goutam","family":"Paul","sequence":"additional","affiliation":[{"name":"Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0419-1858","authenticated-orcid":false,"given":"Vasilios","family":"Zarikas","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRevD.13.191","article-title":"Black holes and thermodynamics","volume":"13","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.physrep.2004.10.003","article-title":"Gravity and the thermodynamics of horizons","volume":"406","author":"Padmanabhan","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"033","DOI":"10.1088\/1126-6708\/2009\/05\/033","article-title":"Holography and thermodynamics of 5D dilaton-gravity","volume":"2009","author":"Kiritsis","year":"2009","journal-title":"J. High Energy Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"L103","DOI":"10.1088\/0305-4470\/12\/5\/007","article-title":"The Quantum Open System as a Model of the Heat Engine","volume":"12","author":"Alicki","year":"1979","journal-title":"J. Phys. A"},{"key":"ref_5","first-page":"031044","article-title":"Equivalence of quantum heat machines, and quantum-thermodynamic signatures","volume":"5","author":"Uzdin","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1063\/1.446862","article-title":"A Quantum Mechanical Open System as a Model of a Heat Engine","volume":"80","author":"Kosloff","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1146\/annurev-physchem-040513-103724","article-title":"Quantum Heat Engines and Refrigerators: Continuous Devices","volume":"65","author":"Kosloff","year":"2014","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4185","DOI":"10.1038\/ncomms5185","article-title":"Work Extraction and Thermodynamics for Individual Quantum Systems","volume":"5","author":"Skrzypczyk","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"090601","DOI":"10.1103\/PhysRevLett.109.090601","article-title":"Quantum Bath Refrigeration Towards Absolute Zero: Challenging the Unattainability Principle","volume":"109","author":"Alicki","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"031105","DOI":"10.1103\/PhysRevE.76.031105","article-title":"Quantum Thermodynamic Cycles and Quantum Heat Engines","volume":"76","author":"Quan","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"030602","DOI":"10.1103\/PhysRevLett.112.030602","article-title":"Nanoscale Heat Engine Beyond the Carnot Limit","volume":"112","author":"Abah","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3949","DOI":"10.1038\/srep03949","article-title":"Quantum-Enhanced Absorption Refrigerators","volume":"4","author":"Correa","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"230601","DOI":"10.1103\/PhysRevLett.110.230601","article-title":"Extracting Quantum Work Statistics and Fluctuation Theorems by Single-Qubit Interferometry","volume":"110","author":"Dorner","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"080402","DOI":"10.1103\/PhysRevLett.108.080402","article-title":"Thermalization in Nature and on a Quantum Computer","volume":"108","author":"Riera","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"203006","DOI":"10.1103\/PhysRevLett.109.203006","article-title":"Single-Ion Heat Engine at Maximum Power","volume":"109","author":"Abah","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"183602","DOI":"10.1103\/PhysRevLett.114.183602","article-title":"All-Optical Nano-mechanical Heat Engine","volume":"114","author":"Dechant","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"150602","DOI":"10.1103\/PhysRevLett.112.150602","article-title":"Quantum Opto-mechanical Heat Engine","volume":"112","author":"Zhang","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"120602","DOI":"10.1103\/PhysRevLett.108.120602","article-title":"Cooling by Heating: Very Hot Thermal Light Can Significantly Cool Quantum Systems","volume":"108","author":"Mari","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","unstructured":"Zurek, W.H. (2003). Maxwell\u2019s demon, Szilard\u2019s engine and quantum measurements. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1007\/BF01341281","article-title":"\u00dcber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen","volume":"53","author":"Szilard","year":"1929","journal-title":"Z. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"070401","DOI":"10.1103\/PhysRevLett.106.070401","article-title":"Quantum Szilard engine","volume":"106","author":"Kim","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1016\/j.aop.2012.08.008","article-title":"Revisiting the quantum Szilard engine with fully quantum considerations","volume":"327","author":"Li","year":"2012","journal-title":"Ann. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.3938\/jkps.61.1187","article-title":"Szilard\u2019s information heat engines in the deep quantum regime","volume":"61","author":"Kim","year":"2012","journal-title":"J. Korean Phys. Soc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"031114","DOI":"10.1103\/PhysRevE.85.031114","article-title":"Multiparticle quantum Szilard engine with optimal cycles assisted by a Maxwell\u2019s demon","volume":"85","author":"Cai","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"052117","DOI":"10.1103\/PhysRevE.90.052117","article-title":"Quantum Szilard engines with arbitrary spin","volume":"90","author":"Zhuang","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bengtsson, J., Nilsson Tengstrand, M., Wacker, A., Samuelsson, P., Ueda, M., Linke, H., and Reimann, S.M. (2017). Supremacy of the quantum many-body Szilard engine with attractive bosons. arXiv.","DOI":"10.1103\/PhysRevLett.120.100601"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kosloff, R., and Rezek, Y. (2017). The quantum harmonic Otto cycle. Entropy, 19.","DOI":"10.3390\/e19040136"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Deffner, S. (2018). Efficiency of harmonic quantum Otto engines at maximal power. Entropy, 20.","DOI":"10.3390\/e20110875"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Bustos-Mar\u00fan, R.A., and Calvo, H.L. (2019). Thermodynamics and steady state of quantum motors and pumps far from equilibrium. Entropy, 21.","DOI":"10.3390\/e21090824"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Meng, Z., Chen, L., and Wu, F. (2020). Optimal power and efficiency of multi-stage endoreversible quantum Carnot heat engine with harmonic oscillators at the classical limit. Entropy, 22.","DOI":"10.3390\/e22040457"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Insinga, A.R. (2020). The quantum friction and optimal finite-time performance of the quantum Otto cycle. Entropy, 22.","DOI":"10.3390\/e22091060"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Dann, R., Kosloff, R., and Salamon, P. (2020). Quantum finite-time thermodynamics: Insight from a single qubit engine. Entropy, 22.","DOI":"10.3390\/e22111255"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"204105","DOI":"10.1063\/1.5096173","article-title":"Quantum thermodynamics and open-systems modeling","volume":"150","author":"Kosloff","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"122597","DOI":"10.1016\/j.physa.2019.122597","article-title":"Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with harmonic oscillators","volume":"537","author":"Chen","year":"2020","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1115\/1.4035021","article-title":"Maximum power from fluid flow by applying the first and second laws of thermodynamics","volume":"139","author":"Diaz","year":"2017","journal-title":"J. Energy Resour. Technol."},{"key":"ref_36","first-page":"1","article-title":"Shortcuts to adiabaticity in a time-dependent box","volume":"2","author":"Boshier","year":"2012","journal-title":"Sci. Rep."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1016\/j.automatica.2013.07.020","article-title":"Optimal shortcuts to adiabaticity for a quantum piston","volume":"49","author":"Stefanatos","year":"2013","journal-title":"Automatica"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"042103","DOI":"10.1103\/PhysRevE.96.042103","article-title":"Exponential bound in the quest for absolute zero","volume":"96","author":"Stefanatos","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"16967","DOI":"10.1038\/s41598-019-53331-x","article-title":"Relativistic quantum heat engine from uncertainty relation standpoint","volume":"9","author":"Chattopadhyay","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2038","DOI":"10.1103\/PhysRevA.53.2038","article-title":"Quantum-state disturbance versus information gain: Uncertainty relations for quantum information","volume":"53","author":"Fuchs","year":"1996","journal-title":"Phys. Rev. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1088\/1742-6596\/36\/1\/016","article-title":"Unconditional security of quantum key distribution and the uncertainty principle","volume":"36","author":"Koashi","year":"2006","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Koashi, M. (2005). Simple security proof of quantum key distribution via uncertainty principle. arXiv.","DOI":"10.1088\/1742-6596\/36\/1\/016"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"032103","DOI":"10.1103\/PhysRevA.68.032103","article-title":"Violation of local uncertainty relations as a signature of entanglement","volume":"68","author":"Hofmann","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_44","unstructured":"Osterloh, A. (2008). Entanglement and its facets in condensed matter systems. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"125117","DOI":"10.1103\/PhysRevB.89.125117","article-title":"Quantifying entanglement with scattering experiments","volume":"89","author":"Marty","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_46","first-page":"117903","article-title":"Characterizing entanglement via uncertainty relations","volume":"9","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1038\/nphoton.2011.35","article-title":"Advances in quantum metrology","volume":"5","author":"Giovannetti","year":"2011","journal-title":"Nat. Photonics"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.physleta.2015.12.015","article-title":"Quantum coherence sets the quantum speed limit for mixed states","volume":"380","author":"Mondal","year":"2016","journal-title":"Phys. Lett. A"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"052331","DOI":"10.1103\/PhysRevA.93.052331","article-title":"Quantum speed limits, coherence, and asymmetry","volume":"93","author":"Marvian","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"453001","DOI":"10.1088\/1751-8121\/aa86c6","article-title":"Quantum speed limits: From Heisenberg\u2019s uncertainty principle to optimal quantum control","volume":"50","author":"Deffner","year":"2017","journal-title":"J. Phys. A"},{"key":"ref_51","first-page":"021031","article-title":"Generalized geometric quantum speed limits","volume":"6","author":"Pires","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"17904","DOI":"10.1364\/OE.25.017904","article-title":"Experimental test of uncertainty relations for general unitary operators","volume":"25","author":"Xiao","year":"2017","journal-title":"Opt. Express"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"160405","DOI":"10.1103\/PhysRevLett.116.160405","article-title":"Experimental test of Heisenberg\u2019s measurement uncertainty relation based on statistical distances","volume":"116","author":"Ma","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1038\/srep02221","article-title":"Experimental violation and reformulation of the Heisenberg\u2019s error disturbance uncertainty relation","volume":"3","author":"Baek","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"052117","DOI":"10.1103\/PhysRevA.95.052117","article-title":"Tighter uncertainty and reverse uncertainty relations","volume":"95","author":"Mondal","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_56","unstructured":"Schiff, L. (1955). Quantum Mechanics, International Series in Pure and Applied Physics, McGraw-Hill."},{"key":"ref_57","unstructured":"Griffiths, D.J. (2005). Introduction to Quantum Mechanics, Pearson Prentice Hall."},{"key":"ref_58","unstructured":"Reif, F. (2009). Fundamentals of Statistical and Thermal Physics, Waveland Press."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"260401","DOI":"10.1103\/PhysRevLett.113.260401","article-title":"Stronger uncertainty relations for all incompatible observables","volume":"113","author":"Maccone","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"2619","DOI":"10.1007\/s10773-019-04150-3","article-title":"Probing Uncertainty Relations in Non-Commutative Space","volume":"58","author":"Chattopadhyay","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Cerone, P., and Dragomir, S.S. (2011). Mathematical Inequalities, Chapman and Hall\/CRC.","DOI":"10.1201\/b10483"},{"key":"ref_62","unstructured":"Saha, M., and Srivastava, B.N. (1935). Treatise on Heat, Longman, Rees, Orme, Brown, Green & Longman."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"3086","DOI":"10.1063\/1.1396831","article-title":"Quantum degeneracy effect on the work output from a Stirling cycle","volume":"90","author":"Saygin","year":"2001","journal-title":"J. Appl. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"012130","DOI":"10.1103\/PhysRevE.88.012130","article-title":"Quantum dynamical framework for Brownian heat engines","volume":"88","author":"Agarwal","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1140\/epjd\/e2013-40536-0","article-title":"Quantum Stirling heat engine and refrigerator with single and coupled spin systems","volume":"68","author":"Huang","year":"2014","journal-title":"Eur. Phys. J. D"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1038\/nphys2163","article-title":"Realization of a micrometre-sized stochastic heat engine","volume":"8","author":"Blickle","year":"2011","journal-title":"Nat. Phys."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"012123","DOI":"10.1103\/PhysRevE.100.012123","article-title":"Quantum heat engine based on level degeneracy","volume":"100","author":"Thomas","year":"2019","journal-title":"Phys. Rev. E"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1038\/s41467-017-01991-6","article-title":"Quantum engine efficiency bound beyond the second law of thermodynamics","volume":"9","author":"Niedenzu","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Plenio, M.B., and Virmani, S. (2014). An introduction to entanglement measures. Quantum Information and Coherence, Springer.","DOI":"10.1007\/978-3-319-04063-9_8"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1088\/0143-0807\/17\/1\/004","article-title":"Relativistic particle in a box","volume":"17","author":"Alberto","year":"1996","journal-title":"Eur. J. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"181602","DOI":"10.1103\/PhysRevLett.96.181602","article-title":"Holographic derivation of entanglement entropy from the anti\u2013de sitter space\/conformal field theory correspondence","volume":"96","author":"Ryu","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1103\/PhysRevD.52.1108","article-title":"Hilbert space representation of the minimal length uncertainty relation","volume":"52","author":"Kempf","year":"1995","journal-title":"Phys. Rev. D"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"012106","DOI":"10.1103\/PhysRevA.81.012106","article-title":"Composite system in deformed space with minimal length","volume":"81","author":"Quesne","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"365204","DOI":"10.1088\/1751-8113\/42\/36\/365204","article-title":"Noncommutative differential forms on the kappa-deformed space","volume":"42","author":"Meljanac","year":"2009","journal-title":"J. Phys. A"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1088\/1367-2630\/8\/5\/083","article-title":"Irreversible performance of a quantum harmonic heat engine","volume":"8","author":"Rezek","year":"2006","journal-title":"New J. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/439\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:27:27Z","timestamp":1760365647000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,9]]},"references-count":75,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["e23040439"],"URL":"https:\/\/doi.org\/10.3390\/e23040439","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,4,9]]}}}