# Fröhlich Condensate: Emergence of Synergetic Dissipative Structures in Information Processing Biological and Condensed Matter Systems

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## Abstract

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## 1. Introduction

“... under appropriate conditions a phenomenon quite similar to a Bose condensation may occur in substances which possess longitudinal electric modes. If energy is fed into these modes and thence transferred to other degrees of freedom of the substance, then a stationary state will be reached in which the energy content of the electric modes is larger than in the thermal equilibrium. This excess energy is found to be channelled into a single mode—exactly as in Bose condensation—provided the energy supply exceeds a critical value. Under these circumstances a random supply of energy is thus not completely thermalized but partly used in maintaining a coherent electric wave in the substance." [1]

## 2. Biology, Physics and Fröhlich Condensate

## 3. Complex Behaviour in Open Boson Systems

**NEFBEC**(short for Non-Equilibrium Fröhlich-Bose-Einstein Condensation for the reasons stated below).

- A first case was evidenced by
**Herbert Fröhlich**who considered, as already noticed, the many boson system consisting of polar vibration (LO-phonons) in bio-polymers under dark excitation (metabolic energy pumping) and embedded in a surrounding fluid [1,2,3,4,7,46]. From a Science, Technology and Innovation (STI) point of view, it was considered to have implications in medical diagnosis [9]. More recently it has been considered to be related to brain functioning and artificial intelligence [47] - A third one is that of excitons (electron-hole pairs in semiconductors) interacting with the lattice vibrations and under the action of RF-electromagnetic fields; on an STI aspect, the phenomenon has been considered for allowing a possible exciton-laser in the THz frequency range called “Excitoner” [18,19];
- A fourth one is the case of magnons [50,51], where the thermal bath is constituted by the phonon system, with which a nonlinear interaction exists, and the magnons are driven arbitrarily out of equilibrium by a source of electromagnetic radio frequency [52]. Technological applications are related to the construction of sources of coherent microwave radiation [53,54].

- 5. A fifth one consists in a system of longitudinal acoustic phonons driven away from equilibrium by means of drifting electron excitation (presence of an electric field producing an electron current), which has been related to the creation of the so-called Saser, an acoustic laser device, with applications in computing and imaging [45,55];

## 4. Non-Equilibrium Thermodynamic Theory of Fröhlich Condensate

**Figure 1.**An atomic model of the -helix structure in a protein and a rough description of the proposed mechanical model (reproduced from [7]).

- standing for the rate of population enhancement due to the action of the pumping source, which involves a positive feedback process that largely improves the efficiency of the pumping source;
- is the contribution arising out of the first term on the right of the interaction of the quasi-particles and the bath in Equation (4);
- is the rate of change arising out of the second term in of Equation (4), the Livshits contribution;
- is the rate of change due to the third term in of Equation (4), the Fröhlich one, which contains linear and bi-linear contributions in the quasi-particle populations (for simplicity we have omitted to make explicit the dependence on in the populations on the right):

**Figure 2.**Populations of the modes in the steady state for , compared with the case of absence of nonlinear interactions. when nonlinear interaction of Equation (15) is present and when neglected (reproduced from [7]).

## 5. Concluding Remarks

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**MDPI and ACS Style**

Vasconcellos, Á.R.; Vannucchi, F.S.; Mascarenhas, S.; Luzzi, R.
Fröhlich Condensate: Emergence of Synergetic Dissipative Structures in Information Processing Biological and Condensed Matter Systems. *Information* **2012**, *3*, 601-620.
https://doi.org/10.3390/info3040601

**AMA Style**

Vasconcellos ÁR, Vannucchi FS, Mascarenhas S, Luzzi R.
Fröhlich Condensate: Emergence of Synergetic Dissipative Structures in Information Processing Biological and Condensed Matter Systems. *Information*. 2012; 3(4):601-620.
https://doi.org/10.3390/info3040601

**Chicago/Turabian Style**

Vasconcellos, Áurea R., Fabio Stucchi Vannucchi, Sérgio Mascarenhas, and Roberto Luzzi.
2012. "Fröhlich Condensate: Emergence of Synergetic Dissipative Structures in Information Processing Biological and Condensed Matter Systems" *Information* 3, no. 4: 601-620.
https://doi.org/10.3390/info3040601