Variational Control of Biophysical Systems: From Action and Frequency to Spectral and Structural Modulation of Biological Processes
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2026
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| _version_ | 1866901972915847168 |
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| author | Jonatan P. Camargo |
| author_facet | Jonatan P. Camargo |
| contents | <p>We present a unified variational formulation in which the dynamics of physical and biophysical systems are described based on the accumulated action \(S\) and its time derivative \(\dot S\). It is shown that the observable frequency emerges as \[ f = \frac{1}{2\pi\hbar}\dot S, \] establishing a direct correspondence between spectroscopy and the action accumulation rate. The analysis of the relative phase between independent systems leads to a discrete compatibility condition, \[ \Delta S(t_n)=2\pi n\hbar, \] from which it follows that physical events occur within finite time windows characterized by \[ \Delta t \sim \frac{\hbar}{|\Delta \dot S|}. \]</p> <p>Applying this framework to molecular systems, we demonstrate that the internal dynamics are governed by a set of spectral modes \(\{\nu_m\}\), with \(\dot S_m = h\nu_m\), and that the coupling to electromagnetic fields is determined by the spectral proximity \(|\nu_m - f_{EM}|\), and not solely by field intensity. In this context, electromagnetic fields are interpreted as experimental channels for accessing the action rate, while chemical interactions act as structural modifications of the internal spectrum.</p> <p>It is further shown that different intervention mechanisms---electromagnetic control and chemical modulation---are equivalent at the variational level, since both act as perturbations on the fundamental quantity \(\Delta \dot S\). This equivalence allows formulating a general principle of control, in which the functional dynamics of biological systems are determined by the modulation of this quantity.</p> <p>In the biophysical regime, enzymes and molecular motors are described as discrete dynamical systems, whose evolution consists of sequences of events conditioned by action compatibility. Molecular structure defines the accessible states, while \(\Delta \dot S\) determines the order and timing of transitions. From this formulation, a falsifiable experimental protocol is proposed, based on the comparison between structural control and spectral control, allowing for the isolation of dynamic effects independent of geometric alterations.</p> <p>As a consequence, pathological states are characterized as deviations in the compatibility dynamics, and therapeutic interventions are interpreted as processes for correcting \(\Delta \dot S\), performed either by electromagnetic modulation or chemical agents. The work thus establishes a non-circular bridge among variational principles, molecular spectroscopy, and biophysical control, providing a mathematically consistent and operationally testable framework for the analysis of complex systems.</p> <p>This work does not replace previous developments, but organizes them into a unified operational framework.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19518453 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Variational Control of Biophysical Systems: From Action and Frequency to Spectral and Structural Modulation of Biological Processes Jonatan P. Camargo <p>We present a unified variational formulation in which the dynamics of physical and biophysical systems are described based on the accumulated action \(S\) and its time derivative \(\dot S\). It is shown that the observable frequency emerges as \[ f = \frac{1}{2\pi\hbar}\dot S, \] establishing a direct correspondence between spectroscopy and the action accumulation rate. The analysis of the relative phase between independent systems leads to a discrete compatibility condition, \[ \Delta S(t_n)=2\pi n\hbar, \] from which it follows that physical events occur within finite time windows characterized by \[ \Delta t \sim \frac{\hbar}{|\Delta \dot S|}. \]</p> <p>Applying this framework to molecular systems, we demonstrate that the internal dynamics are governed by a set of spectral modes \(\{\nu_m\}\), with \(\dot S_m = h\nu_m\), and that the coupling to electromagnetic fields is determined by the spectral proximity \(|\nu_m - f_{EM}|\), and not solely by field intensity. In this context, electromagnetic fields are interpreted as experimental channels for accessing the action rate, while chemical interactions act as structural modifications of the internal spectrum.</p> <p>It is further shown that different intervention mechanisms---electromagnetic control and chemical modulation---are equivalent at the variational level, since both act as perturbations on the fundamental quantity \(\Delta \dot S\). This equivalence allows formulating a general principle of control, in which the functional dynamics of biological systems are determined by the modulation of this quantity.</p> <p>In the biophysical regime, enzymes and molecular motors are described as discrete dynamical systems, whose evolution consists of sequences of events conditioned by action compatibility. Molecular structure defines the accessible states, while \(\Delta \dot S\) determines the order and timing of transitions. From this formulation, a falsifiable experimental protocol is proposed, based on the comparison between structural control and spectral control, allowing for the isolation of dynamic effects independent of geometric alterations.</p> <p>As a consequence, pathological states are characterized as deviations in the compatibility dynamics, and therapeutic interventions are interpreted as processes for correcting \(\Delta \dot S\), performed either by electromagnetic modulation or chemical agents. The work thus establishes a non-circular bridge among variational principles, molecular spectroscopy, and biophysical control, providing a mathematically consistent and operationally testable framework for the analysis of complex systems.</p> <p>This work does not replace previous developments, but organizes them into a unified operational framework.</p> |
| title | Variational Control of Biophysical Systems: From Action and Frequency to Spectral and Structural Modulation of Biological Processes |
| url | https://doi.org/10.5281/zenodo.19518453 |