{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T05:23:39Z","timestamp":1787289819255,"version":"build-2736575974"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T00:00:00Z","timestamp":1787097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007586","name":"Aix-Marseille University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007586","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/035xkbk20","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["FP7-ICT-318121"],"award-info":[{"award-number":["FP7-ICT-318121"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"award":["FP7-ICT-318121"],"award-info":[{"award-number":["FP7-ICT-318121"]}],"id":[{"id":"https:\/\/ror.org\/00k4n6c32","id-type":"ROR","asserted-by":"publisher"}]},{"name":"French CNRS"},{"name":"Occitanie Region"},{"name":"Montpellier University"},{"id":[{"id":"https:\/\/ror.org\/057ap5t09","id-type":"ROR","asserted-by":"publisher"}]},{"name":"LabEx NUMEV","award":["ANR-10-LABX-0020"],"award-info":[{"award-number":["ANR-10-LABX-0020"]}]},{"name":"France-BioImaging national infrastructure","award":["ANR-10-INBS-04"],"award-info":[{"award-number":["ANR-10-INBS-04"]}]},{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["765426"],"award-info":[{"award-number":["765426"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["964203"],"award-info":[{"award-number":["964203"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"award":["765426"],"award-info":[{"award-number":["765426"]}],"id":[{"id":"https:\/\/ror.org\/019w4f821","id-type":"ROR","asserted-by":"publisher"}]},{"award":["964203"],"award-info":[{"award-number":["964203"]}],"id":[{"id":"https:\/\/ror.org\/019w4f821","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We review a theoretical and experimental programme with the aim of understanding two intimately related fundamental phenomena in biophysics: (i) the classical analogue of Fr\u00f6hlich phonon condensation in macromolecules driven out of thermal equilibrium and (ii) the consequent activation of long-range resonant electrodynamic intermolecular forces. Both phenomena are underpinned by explicit Hamiltonian models. The first is derived by applying the time-dependent variational principle (TDVP) to the quantum Wu\u2013Austin model, producing a fully classical Hamiltonian in action-angle variables whose nonlinear rate equations exhibit a nonequilibrium phase transition: the channelling of supplied energy into the lowest-frequency collective mode. The second is grounded in a classical electrodynamic Hamiltonian for two coupled oscillating dipoles whose normal-mode structure predicts long-range (\u223c1\/r3) resonant interactions, absent at thermal equilibrium but activated by out-of-equilibrium collective oscillations. We also discuss a complementary Hamiltonian approach that connects Fr\u00f6hlich\u2019s rate equations directly to Hamilton\u2019s equations of motion, clarifying the role of bath-mediated nonlinear coupling and the conditions for strong condensation at room temperature. In addition, the TDVP is applied to a Davydov\u2013Holstein\u2013Fr\u00f6hlich Hamiltonian describing electron\u2013phonon motion along the backbone of a specific DNA sequence and its cognate restriction enzyme, EcoRI: the time-domain Fourier cross-spectrum of the resulting electron currents exhibits a sharp co-resonance peak for the canonical recognition sequence that disappears upon randomisation, providing a sequence-specific electrodynamic signature of DNA\u2013protein recognition. Experimental evidence from THz near-field spectroscopy, fluorescence correlation spectroscopy, and direct observation of protein clustering is reviewed in relation to these theoretical predictions. The results establish a coherent physical picture suggesting that metabolic energy supply can play a role in driving macromolecules into coherently oscillating states that activate selective, distance-reaching electrodynamic forces capable of contributing to the organisation of biochemical reactions in living matter.<\/jats:p>","DOI":"10.3390\/e28080928","type":"journal-article","created":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T11:04:12Z","timestamp":1787137452000},"page":"928","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review"],"prefix":"10.3390","volume":"28","author":[{"given":"Matteo","family":"Gori","sequence":"first","affiliation":[{"name":"Department of Physics and Sciences of Materials, University of Luxembourg, L-1511 Luxembourg, Luxembourg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Franzosi","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, University of Siena, Via Roma 56, 53100 Siena, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulio","family":"Pettini","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, University of Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy"},{"name":"I.N.F.N., Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1561-4390","authenticated-orcid":false,"given":"Marco","family":"Pettini","sequence":"additional","affiliation":[{"name":"Department of Physics, Aix-Marseille University, 13288 Marseille, France"},{"name":"CNRS Centre de Physique Th\u00e9orique UMR7332, 13288 Marseille, France"},{"name":"Quantum Biology Lab, Howard University, 2400 6th St NW, Washington, DC 20059, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1038\/nrm.2017.7","article-title":"Biomolecular Condensates: Organizers of Cellular Biochemistry","volume":"18","author":"Banani","year":"2017","journal-title":"Nat. Rev. Mol. 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