{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:22:10Z","timestamp":1760149330027,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,30]],"date-time":"2023-07-30T00:00:00Z","timestamp":1690675200000},"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>Using an analogy between the multi-fractal Schr\u00f6dinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates.<\/jats:p>","DOI":"10.3390\/e25081143","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T01:26:40Z","timestamp":1690766800000},"page":"1143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion"],"prefix":"10.3390","volume":"25","author":[{"given":"Decebal","family":"Vasincu","sequence":"first","affiliation":[{"name":"Faculty of Dental Medicine, \u201cGrigore T. Popa\u201d University of Medicine and Pharmacy, 700115 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreea Bianca","family":"Bruma","sequence":"additional","affiliation":[{"name":"Faculty of Physics, \u201dAlexandru Ioan Cuza\u201d University of Iasi, 700506 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oana","family":"Rusu","sequence":"additional","affiliation":[{"name":"Faculty of Material Science and Engineering, \u201cGheorghe Asachi\u201d University of Iasi, 700050 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristina Marcela","family":"Rusu","sequence":"additional","affiliation":[{"name":"Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vlad","family":"Ghizdovat","sequence":"additional","affiliation":[{"name":"Department of Biophysics and Medical Physics, \u201cGrigore T. Popa\u201d University of Medicine and Pharmacy, 700115 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maricel","family":"Agop","sequence":"additional","affiliation":[{"name":"Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania"},{"name":"Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nottale, L. (2011). Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics, Imperial College Press.","DOI":"10.1142\/p752"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Merches, I., and Agop, M. (2016). Differentiability and Fractality in Dynamics of Physical Systems, World Scientific.","DOI":"10.1142\/9606"},{"key":"ref_3","unstructured":"Agop, M., and Paun, V.P. (2017). Fundaments and Applications, Romanian Academy Publishing House."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mandelbrot, B.B. (2004). Fractal and Chaos, Springer.","DOI":"10.1007\/978-1-4757-4017-2"},{"key":"ref_5","unstructured":"Cristescu, C.P. (2008). Theoretical Fundaments and Applications, Romanian Academy Publishing House."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5551","DOI":"10.1103\/PhysRevD.47.5551","article-title":"Minkowski space non-Abelian classical solutions with noninteger winding number change","volume":"47","author":"Farhi","year":"1993","journal-title":"Phys. Rev. D"},{"key":"ref_7","first-page":"182","article-title":"Roughness variation of a nanohybrid composite resin submitted to acid and abrasive challenges","volume":"24","author":"Taraboanta","year":"2020","journal-title":"Int. J. Med. Dent."},{"key":"ref_8","first-page":"755","article-title":"Surface characteristics of restorative composite resins after polishing with profine lamineer tips","volume":"53","author":"Iovan","year":"2016","journal-title":"Mater. Plast."},{"key":"ref_9","first-page":"1144","article-title":"The Assessment of Erosive Potential of Some Acid Beverages on Indirect\u2014Restorative Materials","volume":"67","author":"Tofan","year":"2016","journal-title":"Rev. Chim."},{"key":"ref_10","first-page":"2051","article-title":"The assessment of biological parameters and remineralisation potential of saliva in pregnancy","volume":"66","author":"Pancu","year":"2015","journal-title":"Rev. Chim."},{"key":"ref_11","first-page":"78","article-title":"Study concerning the influence of the finishing and polishing systems on the surface state of various types of composite resins","volume":"5","author":"Stoleriu","year":"2013","journal-title":"Rom. J. Oral Rehabil."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1650153","DOI":"10.1142\/S0217984916501530","article-title":"From Kepler problem to skyrmions","volume":"30","author":"Mazilu","year":"2016","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dittrich, W., and Reuter, M. (2017). Classical, and Quantum Dynamics, Springer.","DOI":"10.1007\/978-3-319-58298-6"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zelikin, M.I. (2000). Control Theory and Optimization, Encyclopaedia of Mathematical Sciences, Springer.","DOI":"10.1007\/978-3-662-04136-9"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1119\/1.1974957","article-title":"Time Translation Invariance for Certain Dissipative Classical Systems","volume":"36","author":"Denman","year":"1968","journal-title":"Am. J. Phys."},{"key":"ref_16","unstructured":"Landau, L.D., and Lifschitz, E.M. (1966). M\u00e9canique, Mir Editions, Moscou Larmor, J. (1900): Aether and Matter, Cambridge University Press."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1142\/S0217751X9900097X","article-title":"Integrability of the Riccati equation from a group-theoretical viewpoint","volume":"14","author":"Carinena","year":"1999","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_18","first-page":"3217","article-title":"Equivalence Classes of Minimum Uncertainty Packets","volume":"D1","author":"Stoler","year":"1970","journal-title":"Phys. Rev."},{"key":"ref_19","first-page":"2309","article-title":"Generalized Coherent States","volume":"D4","author":"Stoler","year":"1971","journal-title":"Phys. Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2745","DOI":"10.1142\/S0217751X88001156","article-title":"The Origins of Skyrmions","volume":"A3","author":"Skyrme","year":"1988","journal-title":"Int. J. Mod. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Brown, G.E. (1994). Selected Papers, with Comentary, World Scientific. World Scientific Series in 20th Century Physics.","DOI":"10.1142\/2251"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Slobodeanu, R. (2009). On the Geometrized Skyrme and Faddeev Models. arXiv.","DOI":"10.1016\/j.geomphys.2009.12.012"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4510","DOI":"10.1103\/PhysRevD.18.4510","article-title":"Harmonic Maps as Models for Physical Theories","volume":"18","author":"Misner","year":"1978","journal-title":"Phys. Rev. D"},{"key":"ref_24","first-page":"127","article-title":"A Non-Linear Field Theory","volume":"A260","author":"Skyrme","year":"1961","journal-title":"Proc. R. Soc. Lond."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.physletb.2004.11.015","article-title":"Skyrmions, Instantons, Mass and Curvature","volume":"605","author":"Atiyah","year":"2004","journal-title":"Phy. Lett. D"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rogers, C., and Schief, W.K. (2002). B\u00e4cklund and Darboux Transformations, Cambridge University Press.","DOI":"10.1017\/CBO9780511606359"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"084049","DOI":"10.1103\/PhysRevD.87.084049","article-title":"Hedgehog ansatz and its generalization for self-gravitating Skyrmions","volume":"87","author":"Canfora","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_28","first-page":"802","article-title":"The Maximal Kinematical Invariance Group of the Free Schr\u00f6dinger Equation","volume":"45","author":"Niederer","year":"1972","journal-title":"Helv. Phys. Acta"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/BF02785666","article-title":"Conformal Invariance in Quantum Mechanics","volume":"34","author":"Fubini","year":"1976","journal-title":"Nuovo Cimento A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/8\/1143\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:22:35Z","timestamp":1760127755000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/8\/1143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,30]]},"references-count":29,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["e25081143"],"URL":"https:\/\/doi.org\/10.3390\/e25081143","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,7,30]]}}}