# Energy from Negentropy of Non-Cahotic Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Different Entropy Contributions

## 3. Clausius and Helmholtz Suggestion

## 4. A Different Subdivision of Free Energy and Entropy

## 5. Transfer of Energy

- -
- Case of exporting entropy

- -
- Case of importing entropy

## 6. An Explicit Example to a Non-Ideal System

- Transition from nonequilibrium to equilibrium by switching off the interaction: from the state $(T,\phantom{\rule{0.166667em}{0ex}}V,\phantom{\rule{0.166667em}{0ex}}N,\phantom{\rule{0.166667em}{0ex}}U(r)\ne 0)$ to $(\widehat{T},\phantom{\rule{0.166667em}{0ex}}V,\phantom{\rule{0.166667em}{0ex}}N,\phantom{\rule{0.166667em}{0ex}}U\left(r\right)=0)$. The energy difference is$$\begin{array}{c}\hfill \Delta E=N\phantom{\rule{0.166667em}{0ex}}\left(\right)open="("\; close=")">\frac{3}{2}\phantom{\rule{0.166667em}{0ex}}k\phantom{\rule{0.166667em}{0ex}}\Delta T+n\phantom{\rule{0.166667em}{0ex}}\Delta C\left(T\right)\phantom{\rule{4pt}{0ex}},\end{array}$$The second term $\Delta C\left(T\right)$ derives from terms containing the interaction $U\left(r\right)$.Let us consider a system in interaction whose potential can be modelled by an average energy value $\langle U\left(r\right)\rangle $ with an interaction radius equal to ${R}_{c}$. Then, Equations (37) and (38) still hold where now$$\begin{array}{c}B\left(T\right)=\frac{2}{3}\phantom{\rule{0.166667em}{0ex}}\pi \phantom{\rule{0.166667em}{0ex}}{R}_{c}^{3}\phantom{\rule{0.166667em}{0ex}}\left(\right)open="("\; close=")">1-exp\left(\right)open="("\; close=")">-\frac{\langle U\left(r\right)\rangle}{k\phantom{\rule{0.166667em}{0ex}}T}\hfill & \phantom{\rule{4pt}{0ex}},\end{array}$$$$\begin{array}{c}C\left(T\right)=\frac{2}{3}\phantom{\rule{0.166667em}{0ex}}\pi \phantom{\rule{0.166667em}{0ex}}\langle U\left(r\right)\rangle \phantom{\rule{0.166667em}{0ex}}{R}_{c}^{3}\phantom{\rule{0.166667em}{0ex}}exp\left(\right)open="("\; close=")">-\frac{\langle U\left(r\right)\rangle}{k\phantom{\rule{0.166667em}{0ex}}T}\phantom{\rule{4pt}{0ex}}.\hfill \end{array}$$When the interaction is switched off, the same amount of energy calculated above can transfer to one element of the system itself (or a cluster of elements) by at most $M\ll N$ elements during a time $\Delta t$ between two successive elastic collisions while the element performs a mean path length. The accelerated element (or cluster) can later give back the acquired energy to other elements. The energy of an element, during the non-equilibrium to equilibrium transition with switching off the interaction or correlation $U\left(r\right)$, fluctuates of the order of $T\phantom{\rule{0.166667em}{0ex}}{S}^{-}/N$ and the energy per particle gained before is $\frac{3}{2}\phantom{\rule{0.166667em}{0ex}}k\Delta T+n\phantom{\rule{0.166667em}{0ex}}\Delta C\left(T\right)$. The bulk properties of the system do not change, however, locally, a modification of the features of the site can be observed.
- Transition from equilibrium state $(T,\phantom{\rule{0.166667em}{0ex}}V,\phantom{\rule{0.166667em}{0ex}}N,\phantom{\rule{0.166667em}{0ex}}U(r)=0)$ to the equilibrium state $(T,\widehat{V},\phantom{\rule{0.166667em}{0ex}}N,\phantom{\rule{0.166667em}{0ex}}U(r)=0)$:$$\begin{array}{c}\hfill \Delta F\equiv \Delta {F}^{-}=N\phantom{\rule{0.166667em}{0ex}}k\phantom{\rule{0.166667em}{0ex}}T\phantom{\rule{0.166667em}{0ex}}ln\left(\right)open="("\; close=")">\frac{\widehat{V}}{V}=-p\phantom{\rule{0.166667em}{0ex}}\Delta V\phantom{\rule{4pt}{0ex}},\end{array}$$$$\begin{array}{c}\hfill Q=-N\phantom{\rule{0.166667em}{0ex}}k\phantom{\rule{0.166667em}{0ex}}T\phantom{\rule{0.166667em}{0ex}}ln\left(\right)open="("\; close=")">\frac{\tilde{V}}{V}\phantom{\rule{4pt}{0ex}},\end{array}$$

## 7. Some Possible Applications

- -
- Molecular gas

- -
- Warm dense matter (a pseudo white dwarf) and nuclear matter

- -
- Liquid metals

- -
- Nuclear reaction in plasmas

- -
- Fluctuations

## 8. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Quarati, P.; Lissia, M.; Scarfone, A.M. Negentropy in the many-body quantum systems. Entropy
**2016**, 18, 63. [Google Scholar] [CrossRef] - Ho, M.-W. What is (Schrödinger’s) negentropy? Mod. Trends Biothermokin
**1994**, 3, 50–61. [Google Scholar] - Mahulikar, S.P.; Herwing, H. Exact thermodynamics principles for dynamic order existence and evolution in chaos. Chaos Solitons Fractals
**2009**, 41, 1939–1948. [Google Scholar] [CrossRef] - Coraddu, M.; Lissia, M.; Quarati, P.; Scarfone, A.M. The role of correlation entropy in nuclear fusion in liquid lithium, indium and mercury. J. Phys. G Nucl. Part. Phys.
**2014**, 41, 125105–125112. [Google Scholar] [CrossRef] - Quarati, P.; Scarfone, A.M. Modified Debye-Huc̎kel electron shielding and penetration factor. APJ
**2007**, 666, 1303–1310. [Google Scholar] [CrossRef] - Dappen, W.; Mussack, K. Dynamic screning in solar and stellar nuclear reactions. Contrib. Plasma Phys.
**2012**, 52, 149–152. [Google Scholar] [CrossRef] - Sato, M. Proposal of an extension of negentropy by Kulback-Leibler information (Definition and exergy). Bull. JSME
**1985**, 28, 2960–2967. [Google Scholar] [CrossRef] - Sato, M. Proposal of an extension of negentropy by Kulback-Leibler information (Proportional relation between negentropy and work). Bull. JSME
**1986**, 29, 837–844. [Google Scholar] [CrossRef] - Chang, Y.-F. Entropy decrease in isolated system and its quantitative calculations in thermodynamics of microstructure. Int. J. Mod. Theor. Phys.
**2015**, 4, 1–15. [Google Scholar] - Chang, Y.-F. Entropy, fluctuation magnified and internal interactions. Entropy
**2005**, 7, 190–198. [Google Scholar] [CrossRef] - Kullback, S.; Leibler, R.A. On Information and sufficiency. Ann. Math. Stat.
**1951**, 22, 79. [Google Scholar] [CrossRef] - Kullback, S. Information Theory and Statistics; John Wiley: New York, NY, USA, 1968. [Google Scholar]
- Gibbs, J.W. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Trans. Conn. Acad. Arts Sci.
**1873**, 2, 382–404. [Google Scholar] - Brillouin, L. The negentropy principle of information. J. Appl. Phys.
**1953**, 24, 1152–1163. [Google Scholar] [CrossRef] - Obukhov, A. Structure of the temperature field in turbulent flows. Izv. Akad. Nauk (Geogr. Geophys. Ser.)
**1949**, 13, 58–69. [Google Scholar] - Clausius, R. Die Mechanische Warmtheorie; Vieweg: Braunschweig, Germany, 1865. (In German) [Google Scholar]
- Helmholtz, H. Wissenschaftliche Abhandlungen, I–III; Teubner: Leipzig, Germany, 1882. (In German) [Google Scholar]
- Ebeling, W.; Sokolov, I.M. Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems; World Scientific: Singapore, 2005. [Google Scholar]
- Walecka, J.D. Introduction to Statistical Mechanics; World Scientific: Singapore, 2011. [Google Scholar]
- Wallace, D.C. Statistical Physics of Crystals and Liquids; World Scientific: Singapore, 2002. [Google Scholar]
- Quarati, P.; Scarfone, A.M. Non-extensive thermostatistics approach to metal melting entropy. Physica A
**2013**, 392, 6512–6522. [Google Scholar] [CrossRef] - Tanaka, S.; Mitake, S.; Yan, X.-Z.; Ichimaru, S. Theory of interparticle correlations in dense, high-temperature plasmas. III. Thermodynamic functions. Phys. Rev. A
**1985**, 32, 1779. [Google Scholar] [CrossRef] - Ichimaru, S. Nuclear fusion in dense plasmas. Rev. Mod. Phys.
**1993**, 65, 255. [Google Scholar] [CrossRef] - Anderegg, F.; Dubin, D.H.; Affolter, M.; Driscoll, C.F. Measurements of correlations enhanced collision rates in the mildly correlated regime (Γ ∼ 1). Phys. Plasmas
**2017**, 24, 09218. [Google Scholar] [CrossRef] - Szilard, L. Über die entropieverminderung in einem thermodynamischen system bei eingriffen intelligenter wesen. Z. Phys.
**1929**, 53, 840. [Google Scholar] [CrossRef] - Schrödinger, E. What Is Life? Cambridge University Press: Cambridge, UK, 1945. [Google Scholar]
- Brillouin, L. Science and Information Theory; Academic Press: New York, NY, USA, 1962. [Google Scholar]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Quarati, P.; Scarfone, A.M.; Kaniadakis, G.
Energy from Negentropy of Non-Cahotic Systems. *Entropy* **2018**, *20*, 113.
https://doi.org/10.3390/e20020113

**AMA Style**

Quarati P, Scarfone AM, Kaniadakis G.
Energy from Negentropy of Non-Cahotic Systems. *Entropy*. 2018; 20(2):113.
https://doi.org/10.3390/e20020113

**Chicago/Turabian Style**

Quarati, Piero, Antonio M. Scarfone, and Giorgio Kaniadakis.
2018. "Energy from Negentropy of Non-Cahotic Systems" *Entropy* 20, no. 2: 113.
https://doi.org/10.3390/e20020113