Pith. sign in

REVIEW 4 major objections 3 minor 32 references

Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review

T0 review · 4 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This review argues that metabolic or photonic energy can drive macromolecules into coherent collective oscillations, and presents experimental evidence that these oscillations produce long-range 1/r^3 resonant electrodynamic forces between

desk verdict A clear self-review of the Pettini Fröhlich programme: theory well presented, but the experimental identification of collective modes is circular and lacks artifact controls. read the letter →

arxiv 2607.20508 v1 pith:LMOXBOBZ submitted 2026-07-03 physics.bio-ph

Matteo Gori , Roberto Franzosi , Giulio Pettini , Marco Pettini This is my paper · ORCID
classification physics.bio-ph
keywords phononcondensationFröhlicheffectlong-rangeelectrodynamicforcestime-dependentvariationalprincipleTHzspectroscopyDNA–proteinrecognitionnonequilibriumphasetransitionproteinclustering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reviews a theoretical and experimental programme claiming that an out-of-equilibrium macromolecule, supplied with energy above a threshold, channels that energy into its lowest-frequency collective vibrational mode—a classical analogue of Fröhlich phonon condensation. This coherent oscillation acts as a giant oscillating dipole, and two such coherent molecules feel a resonant 1/r^3 attraction that is absent at thermal equilibrium, where it is replaced by a short-range 1/r^6 van der Waals tail. The authors show that these results follow from explicit Hamiltonians derived through the time-dependent variational principle, and they report supporting observations: sharp sub-THz absorption peaks in laser-pumped BSA and R-PE, threshold and saturation behavior, linear concentration-dependent frequency shifts, and a reversible protein-clustering transition. The same machinery applied to electron–phonon dynamics on DNA and its cognate enzyme EcoRI yields a sharp co-resonance peak in the electron-current cross-spectrum only for the canonical recognition sequence. If correct, the picture assigns metabolic energy a direct mechanistic role in selective, long-range biomolecular recognition.

What carries the argument

The central mathematical machinery is the time-dependent variational principle (TDVP), which turns a quantum Hamiltonian into a fully classical one by extremalizing the action on a manifold of product coherent states. Applied to the Wu–Austin model, it yields a classical Hamiltonian in action-angle variables (J_ω, θ_ω) with J_ω = ħ n_ω, and the Koopman–von Neumann reformulation of the Liouville equation produces nonlinear rate equations whose stationary solutions exhibit a nonequilibrium bifurcation into the lowest-frequency mode. For the two-dipole problem, the load-bearing identity is the resonant normal-mode splitting ω_{i,±}(r) ≃ ω0 ± √(ζ_A ζ_B) χ′_{ii}(r, ω0)/(2ω0), which makes the inte

What would settle it

Check whether the 0.314 THz BSA feature appears when the dye is free in solution or when labelled protein is illuminated at powers below the predicted threshold; either observation would falsify the phonon-condensation assignment. More directly, vary protein radius or Young modulus (e.g., via mutants or osmolytes) and verify that the resonance frequency follows the spheroid-mode formula; if the line does not shift with R_H or E, it is not a collective deformation mode. For the electronic channel, place a single silent mutation that preserves binding but changes the EIIP spectrum: the paper's m

Watch

Extended reading notes

Core claim

The paper's central claim is that classical Hamiltonian mechanics, obtained by dequantizing quantum models with the time-dependent variational principle, describes two real biophysical phenomena: the channelling of supplied energy into the lowest-frequency collective mode of a macromolecule (phonon condensation), and the resulting activation of long-range resonant electrodynamic forces. At resonance, the interaction potential scales as 1/r^3 in the near zone and 1/r in the far zone; at thermal equilibrium the same calculation gives only a 1/r^6 free energy because the action-difference term J_+ − J_− vanishes at first order. The review asserts that this theoretical picture is experimentally

Load-bearing premise

The load-bearing premise is that the sharp THz features observed under illumination (0.314 THz in BSA; 71 and 96 GHz in R-PE) are global collective deformation modes of the whole protein, created by a genuinely out-of-equilibrium coherent state, rather than local dye, solvent, heating, or photochemical artifacts.

Editorial extensions

If this is right

  • If correct, enzyme–substrate encounters in cells could be guided by frequency-matched 1/r^3 forces, changing how reaction kinetics and specificity are modeled.
  • The threshold and saturation behavior of the THz absorption gives a direct experimental signature of the condensation transition; measuring it in other proteins would test how generic the phenomenon is.
  • The sequence-specific co-resonance peak offers a new, testable spectroscopic signature of DNA–protein recognition, potentially independent of binding-affinity measurements.
  • The reversible clustering transition driven by electrodynamic forces provides a physical mechanism for biomolecular condensate formation that is distinct from multivalent phase separation.
  • The position-space Hamiltonian provides a route to atomistic molecular dynamics that could decide whether realistic force fields support condensation at 300 K.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • [Editorial extension] If the 1/r^3 force is real, it should be detectable in biochemical observables such as concentration-dependent shifts in reaction rates or equilibrium constants; the authors' frequency-shift data make this a quantitative prediction.
  • [Editorial extension] The electronic-channel co-resonance predicts that cognate protein–nucleic-acid pairs beyond EcoRI (e.g., transcription factors and their motifs) should show similar cross-spectral peaks that track sequence spectrum rather than binding affinity.
  • [Editorial extension] A systematic scan of the BSA resonance frequency across proteins of known Young modulus and radius would directly test the collective-mode assignment, since Eq. (39) fixes the scaling of ν0 with E and R_H.
  • [Editorial extension] The claim that long-range forces vanish at equilibrium implies that the 1/r^3 frequency shift should decay on a measurable timescale after the laser is switched off; time-resolved measurement of this transient would separate coherent-state physics from static concentration artifacts.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper is a review of a theoretical and experimental programme whose central claim is that biologically supplied (or laser-supplied) energy can drive macromolecules into an out-of-equilibrium, coherent collective oscillation — a classical analogue of Fröhlich phonon condensation — and that the resulting giant oscillating dipoles activate long-range, resonant 1/r^3 electrodynamic forces between biomolecules. The theoretical part derives classical Hamiltonians from quantum models via the time-dependent variational principle: the Wu–Austin model yields action-angle Hamiltonians and Fröhlich-like rate equations with a nonequilibrium condensation transition; a position-space Hamiltonian is simulated to recover condensation at room temperature; and a Davydov–Holstein–Fröhlich model for DNA–EcoRI is used to predict a sequence-specific electron-current co-resonance. The experimental part reviews THz near-field spectroscopy on BSA and R-PE, fluorescence correlation spectroscopy on R-PE clustering, and concentration-dependent frequency shifts, concluding that the observed phenomena support the proposed coherent-oscillation and long-range-force picture.

Significance. If the central experimental identifications are correct, the review consolidates a substantial and provocative programme: it provides a classical Hamiltonian underpinning for Fröhlich's ideas, derives a clean distinction between equilibrium (1/r^6) and out-of-equilibrium (1/r^3) interactions, and connects these to a new electrodynamic mechanism for biomolecular recognition. The TDVP/KvN formalism is elegant and clearly presented, and the reported reproducibility of the BSA THz feature across two laboratories, as well as the reversibility of the R-PE clustering transition, are notable strengths. However, the experimental pillar rests on mode assignments that are not uniquely established, and several 'quantitative' comparisons rely on adjustable parameters. The paper would be more convincing if it distinguished more sharply between established results, model-dependent inferences, and conjectures.

major comments (4)
  1. [VIII.3] The R-PE 71 GHz collective-mode assignment is weakened by a circular inversion. The text states that the mode is 'consistent with the lowest extension mode of a torus' and then obtains E≈5.3 GPa by inverting the Blevins formula from that very mode. This does not validate the assignment; it merely re-expresses the observed frequency in terms of an elastic parameter. The only independent check offered is the 96/71≈1.35 ratio versus √2≈1.41, a single datum without quoted error bars. Please provide an independently measured Young modulus or an independent prediction of both mode frequencies, or explicitly state that the torus-mode interpretation is one possible model rather than a confirmed identification.
  2. [VIII.2] The identification of the 0.314 THz BSA feature as the l=2 spheroidal mode of the whole protein is underdetermined by the controls described. The feature appears only when Alexa 488 is covalently bound and the laser is on, but the text does not report controls that exclude a dye-localized vibrational mode or a local photothermal modification of the protein near the attachment sites. The two weaker resonances at 0.278 and 0.285 THz are 'tentatively' assigned to torsional modes predicted at 0.257 and 0.246 THz, leaving discrepancies of about 8–16% that are attributed to non-spherical shape without quantitative modelling. Since this is the primary experimental evidence for phonon condensation, the assignment needs stronger support or the claim needs to be correspondingly weakened.
  3. [VIII.5, Fig. 14] The claimed 'quantitative' agreement for the concentration-dependent frequency shifts is based on theoretical curves computed with different values of molecular dipole moments (see Fig. 14 caption and Supplementary Materials). With an adjustable dipole moment, the data primarily demonstrate linearity in concentration, not a parameter-free confirmation of the 1/r^3 amplitude. Please state the fitted dipole values, compare them with independent estimates, and provide uncertainties on the experimental slopes; otherwise, this should be described as consistency with the model, not quantitative validation.
  4. [II.1.2, Eq. (7)] The quartic term is introduced to stabilise the Wu–Austin Hamiltonian, and the text asserts that it 'does not alter the condensation mechanism.' This is a load-bearing assumption for the subsequent rate equations, since the original Hamiltonian has no finite ground state. No derivation or quantitative argument is given for why the quartic stabilisation leaves the condensation mechanism unchanged. Please either supply the argument or explicitly label this as an assumption of the reviewed programme.
minor comments (3)
  1. [VIII.2] The estimate of the onset timescale relies on balancing the optical input power with bremsstrahlung losses and yields a very large effective dipole of 14,500–23,000 D with an effective charge of 290–460 elementary charges. This is an order-of-magnitude estimate with several broad assumptions; it should be presented as such and its sensitivity to the assumed number of absorbed photons per fluorophore should be indicated.
  2. [VII.5] The DNA–EcoRI co-resonance at 20–29 THz is obtained from numerical simulation, not from experiment. The phrase 'quantitative agreement with the RRM prediction' is stronger than what is shown, since the RRM itself is an empirical spectral method; rephrasing as 'agreement with the RRM value' would be more precise.
  3. [General / VII.2] There are several typographical and formatting issues, e.g. 'paqrticle-particle' in Sec. VII.2, and inconsistent use of diacritics such as 'Fr¨ohlich' in the text. These should be corrected in a final polish.

Circularity Check

2 steps flagged · score 5.0 of 10

Core TDVP/Fröhlich derivation and BSA 0.308 THz prediction are non-circular, but two experimental consistency checks in the R-PE and frequency-shift sections are parameter fits presented as support.

  1. fitted input called prediction [Sec. VIII.3, R-PE phonon condensation / torus-mode assignment]
    "The collective mode frequency is consistent with the lowest extension mode of a torus of major radius R=37.5 Å and minor radius r=30 Å, yielding a Young modulus E≈5.3 GPa by inversion of the Blevins formula [30], a value that lies squarely between those of myoglobin (3.5 GPa) and BSA (6.75 GPa), both predominantly α-helical proteins like R-PE."

    The 71 GHz peak is inserted into the torus-mode formula to solve for E, so the 'agreement' between the observed peak and the mode assignment is imposed by construction rather than predicted. The only empirical residue is that the fitted E falls in a plausible protein range, which is a weak consistency check. Presenting this as support for identifying the 71 GHz feature as the phonon-condensation collective mode is a fitted input doing evidential work.

  2. fitted input called prediction [Sec. VIII.5, frequency shifts / Fig. 14 caption]
    "Purple squares and orange stars refer to theoretical outcomes worked out with different values of molecular dipole moments (see Supplementary Materials). The steepening of the slope with laser power is also quantitatively consistent with theory: a larger oscillation amplitude generates a larger oscillating dipole moment and hence a stronger electrodynamic coupling."

    In Eq. (22), the interaction energy—and hence the predicted frequency shift—is proportional to the normal-mode action difference set by the oscillating dipole moment. The paper explicitly allows 'different values of molecular dipole moments' for the theoretical curves, meaning the absolute shift amplitude is tuned to the data. The 1/r^3 concentration dependence is still a real prediction, but the claimed quantitative match of the shift magnitude is a fit, not a first-principles outcome.

full rationale

The formal derivation chain is not circular. Eq. (12) is the TDVP expectation value of the Wu–Austin Hamiltonian; Eq. (14) follows from the stated KvN second-order expansion; Eq. (22) gives U(r) from the normal-mode frequency shifts; and the equilibrium cancellation of the 1/r^3 term is argued from the action difference, not assumed by definition. The BSA test is a genuine prediction: Eq. (39) with independently measured E=6.75 GPa and R_H=35 Å gives 0.308 THz against 0.314 THz observed. The self-citations (Refs. [10,11,30]) are to the authors' own prior papers, but the review reproduces the essential equations and the BSA check is parameter-free, so they are not load-bearing as external authority. The circularity concerns are confined to two experimental consistency steps: the R-PE Young modulus is recovered from the very 71 GHz peak it is used to validate, and the theoretical frequency-shift magnitude is computed with adjustable molecular dipole moments. These are partial fits within the experimental pillar; they do not by construction force the condensation transition itself, which has independent, parameter-free support in the BSA prediction and in the numerical rate-equation analysis. On the instructions' scale this warrants a 5, not a 6+: the central derivation has independent content while some supporting 'agreements' reduce to fitted parameters. Possible dye-localized or photothermal artifacts are a correctness risk, not a circularity finding.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No genuinely new particles, mediators, forces, or dimensions are introduced: the proposed long-range interaction is standard electromagnetism activated by a non-thermal population of normal modes. The 'condensate' and 'giant oscillating dipole' are states of existing physical modes, not new entities with independent falsifiable handles.

free parameters (4)
  • R-PE Young modulus E = ≈5.3 GPa
    Obtained by inverting the Blevins torus-mode formula to match the observed 71 GHz mode (Sec. VIII.3), then used as an internal consistency check rather than an independent input.
  • Effective dipole moments for frequency-shift predictions = not disclosed (Supplementary of Ref. [30])
    Fig. 14 theoretical curves are computed with 'different values of molecular dipole moments'; this tunes the 1/r^3 slope to the data instead of providing a parameter-free prediction.
  • Dimensionless rate-equation parameters B, C, quartic couplings = B=1, C=0.1, Υ=10^-4
    Chosen for numerical demonstration of the condensation bifurcation (Fig. 2); the qualitative conclusion is not sensitive to them, but the threshold location is.
  • BSA effective oscillating charge/dipole = Z≈290–460 e; 14,500–23,000 Debye
    Inferred by balancing optical input against bremsstrahlung losses in Sec. VIII.2; used as evidence of a giant dipole but not directly measured.
assumptions (5)
  • standard math TDVP restricted to product coherent states yields a faithful classical Hamiltonian for the quantum model
    Used in Sec. III to derive Eq. (12); valid as a variational mean-field reduction, but not an exact classical limit.
  • domain assumption Born-Markov second-order perturbation theory is applicable to the classical Liouville/KvN dynamics of the bath
    Sec. III.2-III.3; needed to obtain closed rate equations Eq. (14) from the Hamiltonian.
  • ad hoc to paper The quartic stabilising term makes the Wu-Austin Hamiltonian physically well posed and does not alter the condensation mechanism
    Introduced in Sec. II.1.2/Ref. [14]; its form and coefficients are selected to bound the energy, not derived from a microscopic model.
  • domain assumption Debye screening is ineffective for oscillating fields above ~250 MHz in physiological saline
    Sec. V.1; needed for the fields to propagate at sub-THz frequencies; the review cites Ref. [11] rather than deriving or testing it.
  • domain assumption Optical pumping of fluorophores transfers absorbed photon energy into low-frequency protein modes via the 'proteinquake' mechanism
    Sec. VIII.1-VIII.2; load-bearing for interpreting laser experiments as out-of-equilibrium phonon condensation rather than local heating/dye effects.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review." pith.science (2026). https://pith.science/paper/LMOXBOBZ

@misc{pith2026260720508,
  author       = {Pith},
  title        = {Pith review of: Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMOXBOBZ}},
  note         = {Machine review of arXiv:2607.20508}
}
read the original abstract

We review a theoretical and experimental programme addressing two closely related phenomena in biophysics: the classical analogue of Fr\"ohlich phonon condensation in macromolecules driven out of thermal equilibrium, and the resulting activation of long-range resonant electrodynamic intermolecular forces.The first is obtained by applying the time-dependent variational principle (TDVP) to the quantum Wu-Austin model,yielding a fully classical Hamiltonian in action-angle variables whose nonlinear rate equations display a nonequilibrium phase transition: supplied energy is channelled into the lowest-frequency collective mode. The second is based on a classical electrodynamic Hamiltonian for two coupled oscillating dipoles, whose normal modes predict long-range (1/r^3) resonant interactions. These are absent at thermal equilibrium but emerge under out-of-equilibrium coherent oscillations.We also discuss how to link Fr\"ohlich rate equations directly to Hamilton equations, clarifying the role of bath-mediated nonlinear couplings and the conditions for strong condensation at room temperature.In addition, TDVP is applied to a Davydov-Holstein-Fr\"ohlich model describing electron-phonon dynamics along a specific DNA sequence and its cognate restriction enzyme EcoRI. The time-domain Fourier cross-spectrum of the resulting electron currents shows a sharp co-resonance peak for the canonical recognition sequence, which disappears under randomisation, providing a sequence-specific electrodynamic signature of DNA-protein recognition.Experimental evidence from THz near-field spectroscopy, fluorescence correlation spectroscopy, and direct protein clustering is reviewed. Together these results support the view that metabolic energy can drive macromolecules into coherent oscillatory states, activating selective long-range electrodynamic forces relevant to biochemical organisation in living matter.

Figures

Figures reproduced from arXiv: 2607.20508 by the authors.

Figure 1
Figure 1. Classical Fr¨ohlich-like condensation. Normalized energy fractions pi in the normal modes vs. mode frequencies ωi , for N = 20 modes. As the energy input rate S increases, deviations from equipartition grow progressively. Panels (a)–(d) correspond to S = 0.1 (blue), 1 (green), 10 (purple), and 100 (pink). Equipartition gives equal bar heights; note the increasing concentration of energy in the lowest-frequency mode … view at source ↗
Figure 2
Figure 2. Classical Fr¨ohlich-like condensation. Condensation index Ey (left panel) and ratio p1/p0 (right panel) vs. energy input rate S, for increasing mode number Nsys: from right to left curves N = 11, 21, 41, 101, 301.At equipartition Ey = 0, p1/p0 = 1; at full condensation Ey = 1, p1/p0 = 0. The dashed oblique line marks the inflection tangent as a guide to a possible asymptotic bifurcation. From Ref.[10]. into a macros… view at source ↗
Figure 3
Figure 3. Condensation index ρ of a Fr¨ohlich system from Hamiltonian dynamics, for coupling coefficients λijk under three resonance conditions: ωi −ωj ±ω (B) k = 0 (Fr¨ohlich), ωi +ωj −ω (B) k = 0 (Lifshits), and ωi ± ωj ± ω (B) k = 0 (combined). From Ref.[12] [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Time evolution of total energies (kinetic + potential) in a Fr¨ohlich system of nine protein modes (first five shown), computed as 300 ns moving averages from Hamiltonian dynamics. Parameters: bath T = 300 K, source TS = 3000 K, protein frequencies ω1 = 0.2 THz to ω9 =…
Figure 5
Figure 5. Figure 5: Cross frequency spectra between a DNA strand with N1 = 66 nucleotides and the EcoRI enzyme with N2 = 276 amino acids. Panels show DNA strand containing a) the canonical target CTTAAG recognition site, b) cyclic permutation of restriction site in a) to AGCTTA, c) one-nu…
Figure 6
Figure 6. Figure 6: Cross frequency spectra between a DNA strand and the EcoRI enzyme, under the same substrate and initial conditions of [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]
Figure 7
Figure 7. Figure 7: Cross frequency spectra between a DNA strand and the EcoRI enzyme, under the same substrate and initial conditions of [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: Cross frequency spectra between the original substrate and the EcoRI mutants with the single point mutations; a) Ala138 → T hr; b) Glu192 → Lys; c) His114 → T yr; and d) Asp91 → Asn. The initial conditions are the same of [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]
Figure 9
Figure 9. Figure 9: Long-range electrodynamic interactions - Principle and experimental approaches At thermal equilibrium, macromolecules show a Brownian diffusive motion in solution (left panel). By switching-on an external energy source, molecules are in an out-of-thermal equilibrium co…
Figure 10
Figure 10. Figure 10: Differential transmission and absorption spectra as functions of the frequency. Com￾parison of the two normalized spectra for the longest illumination durations. From Ref.[10]. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]
Figure 11
Figure 11. Figure 11: Threshold-like behaviour of giant dipolar oscillations. (a) Intensity of the resonant peak measured at 0.314 THz as a function of the optical laser power. (b) Normalized energy of the fundamental mode calculated as a function of the normalized source power. The differ…
Figure 12
Figure 12. Figure 12: R-PE coherent vibrational states. Comparison of the R-PE in saline solution (purple) and saline solution without R-PE (black). Two collective extension modes of R-PE appear at 71 GHz and 96 GHz. Experimental data (full circles); Lorentz fit (solid line). From Ref.[30]…
Figure 13
Figure 13. Figure 13: Effect of protein concentration and laser power illumination on R-PE diffusion: Clus￾tering phase transition. (a) Diffusion coefficients normalized to the Brownian D0 values measured for each data series at 0.223 µM (⟨r⟩ ≃ 1950 A˚) and recorded at 50 µW (blue circles)…
Figure 14
Figure 14. Figure 14: Frequency shifts of the intramolecular collective vibrations of R-PE and BSA at different concentrations. Measurements were performed at room temperature in aqueous solution with 200 mM of NaCl. Panel (a) refers to R-PE. The shift is relative to the reference frequenc…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references

  1. [1]

    S. F. Banani, H. O. Lee, A. A. Hyman, and M. K. Rosen,Biomolecular Condensates: Orga- nizers of Cellular Biochemistry, Nat. Rev. Mol. Cell Biol.18, 285 (2017)

    2017

  2. [2]

    Berry, C

    J. Berry, C. P. Brangwynne, and M. Haataja,Physical Principles of Intracellular Organization via Active and Passive Phase Transitions, Rep. Prog. Phys.81, 046601 (2018)

    2018

  3. [3]

    L. J. Sweetlove and A. R. Fernie,The Role of Dynamic Enzyme Assemblies and Substrate Channelling in Metabolic Regulation, Nat. Commun.9, 2136 (2018)

    2018

  4. [4]

    Fr¨ ohlich,Long-Range Coherence and Energy Storage in Biological Systems, Int

    H. Fr¨ ohlich,Long-Range Coherence and Energy Storage in Biological Systems, Int. J. Quantum Chem.2, 641 (1968)

    1968

  5. [5]

    Fr¨ ohlich,Long Range Coherence and the Action of Enzymes, Nature (London)228, 1093 (1970)

    H. Fr¨ ohlich,Long Range Coherence and the Action of Enzymes, Nature (London)228, 1093 (1970)

    1970

  6. [6]

    Fr¨ ohlich,Selective Long Range Dispersion Forces between Large Systems, Phys

    H. Fr¨ ohlich,Selective Long Range Dispersion Forces between Large Systems, Phys. Lett. A39, 153 (1972). 36

    1972

  7. [7]

    Fr¨ ohlich,Long-Range Coherence in Biological Systems, Riv

    H. Fr¨ ohlich,Long-Range Coherence in Biological Systems, Riv. Nuovo Cimento7, 399 (1977)

    1977

  8. [8]

    T. M. Wu and S. Austin,Bose Condensation in Biosystems, Phys. Lett. A64, 151 (1977)

    1977

Show all 32 references
  1. [9]

    T. M. Wu and S. Austin,Bose-Einstein Condensation in Biological Systems, J. Theor. Biol. 71, 209 (1978)

    1978

  2. [10]

    Nardecchia, M

    I. Nardecchia, M. Pettiniet al.,Out-of-Equilibrium Collective Oscillation as Phonon Conden- sation in a Model Protein, Phys. Rev. X8, 031061 (2018)

    2018

  3. [11]

    Preto, M

    J. Preto, M. Pettini, and J. A. Tuszynski,Possible Role of Electrodynamic Interactions in Long-Distance Biomolecular Recognition, Phys. Rev. E91, 052710 (2015)

    2015

  4. [12]

    Preto, E

    J. Preto, E. Floriani, V. Calandrini, G. Katona, M. Pettini,Hamiltonian model for en- ergy condensation in classical systems: Relevance to proteins, Phys.Rev.Research8, L022016 (2026)

    2026

  5. [13]

    Faraji, V

    E. Faraji, V. Calandrini, P. Kurian, R. Franzosi, S. Mancini, E. Floriani, G. Pettini, and M. Pettini,Electrodynamic Forces Driving DNA–Protein Interactions at Large Distances, Front. Phys.20, 061200 (2025)

    2025

  6. [14]

    Bolterauer,Elementary Arguments that the Wu–Austin Hamiltonian has no Finite Ground State, Bioelectrochem

    H. Bolterauer,Elementary Arguments that the Wu–Austin Hamiltonian has no Finite Ground State, Bioelectrochem. Bioenerg.48, 301 (1999)

    1999

  7. [15]

    Kramer and M

    P. Kramer and M. Saraceno,Geometry of the Time-Dependent Variational Principle in Quan- tum Mechanics, inGroup Theoretical Methods in Physics(Springer, 1980), pp. 112–121

    1980

  8. [16]

    Kramer,A Review of the Time-Dependent Variational Principle, J

    P. Kramer,A Review of the Time-Dependent Variational Principle, J. Phys. Conf. Ser.99, 012009 (2008)

    2008

  9. [17]

    Jauslin and D

    H.-R. Jauslin and D. Sugny,Dynamics of Mixed Classical-Quantum Systems, Geometric Quan- tization and Coherent States, inMathematical Horizons for Quantum Physics, IMS-NUS Lec- ture Notes, Vol. 20 (World Scientific, 2010)

    2010

  10. [18]

    B. O. Koopman,Hamiltonian Systems and Transformation in Hilbert Space, Proc. Natl. Acad. Sci. U.S.A.17, 315 (1931)

    1931

  11. [19]

    von Neumann,Zur Operatorenmethode in der klassischen Mechanik, Ann

    J. von Neumann,Zur Operatorenmethode in der klassischen Mechanik, Ann. Math.33, 587 (1932)

    1932

  12. [20]

    J. R. Reimers, L. K. McKemmish, R. H. McKenzie, A. E. Mark, and N. S. Hush,Weak, Strong, and Coherent Regimes of Fr¨ ohlich Condensation and Their Applications to Terahertz Medicine and Quantum Consciousness, Proc. Natl. Acad. Sci. U.S.A.106, 4219 (2009). 37

    2009

  13. [21]

    Haken,Cooperative Phenomena in Systems Far from Thermal Equilibrium and in Non- physical Systems, Rev

    H. Haken,Cooperative Phenomena in Systems Far from Thermal Equilibrium and in Non- physical Systems, Rev. Mod. Phys.47, 67 (1975)

    1975

  14. [22]

    Cosic,Macromolecular Bioactivity: Is it Resonant Interaction between Macromolecules? Theory and Applications, IEEE Trans

    I. Cosic,Macromolecular Bioactivity: Is it Resonant Interaction between Macromolecules? Theory and Applications, IEEE Trans. Biomed. Eng.41, 1101 (1994)

    1994

  15. [23]

    Veljkovic, I

    V. Veljkovic, I. Cosic, B. Dimitrijevic, and D. Lalovic,Is it Possible to Analyze DNA and Protein Sequences by the Methods of Digital Signal Processing?, IEEE Trans. Biomed. Eng. 32, 337 (1985)

    1985

  16. [24]

    Giese,Long-Distance Charge Transport in DNA: The Hopping Mechanism, Acc

    B. Giese,Long-Distance Charge Transport in DNA: The Hopping Mechanism, Acc. Chem. Res.33, 631 (2000)

    2000

  17. [25]

    H. B. Gray and J. R. Winkler,Electron Transfer in Proteins, Annu. Rev. Biochem.65, 537 (1996)

    1996

  18. [26]

    Faraji, R

    E. Faraji, R. Franzosi, S. Mancini, and M. Pettini,Transition between Random and Periodic Electron Currents on a DNA Chain, Int. J. Mol. Sci.22, 7361 (2021)

    2021

  19. [27]

    Cosic,The Resonant Recognition Model of Macromolecular Bioactivity: Theory and Appli- cations(Birkh¨ auser, Basel, 1997)

    I. Cosic,The Resonant Recognition Model of Macromolecular Bioactivity: Theory and Appli- cations(Birkh¨ auser, Basel, 1997)

    1997

  20. [28]

    Kurian, A

    P. Kurian, A. Capolupo, T. J. A. Craddock, and G. Vitiello,Water-Mediated Correlations in DNA-Enzyme Interactions, Phys. Lett. A382, 33 (2018)

    2018

  21. [29]

    Ansari, J

    A. Ansari, J. Berendzen, S. F. Bowne, H. Frauenfelder, I. E. Iben, T. B. Sauke, E. Shyamsun- der, and R. D. Young, Proc. Natl. Acad. Sci. U.S.A.82, 5000 (1985)

    1985

  22. [30]

    Lechelon, M

    M. Lechelon, M. Pettiniet al.,Experimental Evidence for Long-Distance Electrodynamic In- termolecular Forces, Sci. Adv.8, eabl5855 (2022)

    2022

  23. [31]

    Perticaroli, J

    S. Perticaroli, J. D. Nickels, G. Ehlers, H. O’Neill, Q. Zhang, and A. P. Sokolov,Secondary Structure and Rigidity in Model Proteins, Soft Matter9, 9548 (2013)

    2013

  24. [32]

    Zhang, G

    Z. Zhang, G. S. Agarwal, and M. O. Scully,Quantum Fluctuations in the Fr¨ ohlich Condensate of Molecular Vibrations Driven Far from Equilibrium, Phys. Rev. Lett.122, 158101 (2019). 38

    2019

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.