# Structuring Information and Entropy: Catalyst as Information Carrier

## Abstract

**:**

## Introduction : Entropy and Information revisited

_{B}ln(W)

_{B}is known as Boltzmann’s constant = 1.38 x 10

^{-23}J/molecule.K

_{i}being the probability of an elementary state characterized by its level of energy as well as by its spatial conformation.

_{B}leads to express entropy as J/molecule.K.

_{B}was not used in this formulation.

_{i}via the following expression:

_{i}being the frequency of use, or probability of appearance, of the symbols x

_{i}used to write the message. The set of all of the symbols x

_{i}constitutes the alphabet used.

_{i}linked to an event with a probability of appearance p

_{i}can be evaluated using the following expression:

_{i}= -log

_{2}(p

_{i})

**bit**and corresponds to a probability of occurrence of the event of 1/2.

^{N}; therefore the complexity is given by:

^{N})

^{N}) to 0.

_{i}(i=1 to n). The complexity C’ of the new set thus modified is then calculated as follows:

_{i}!) (i=1…n)

_{i}!)

_{i}=N

_{i}/N

_{1}=25 (black) N

_{2}=20 (white) N

_{3}=40 (red) N

_{4}=15 (green)

Disorder, Chaos ----------------→ | Order |

Entropy + Negentropy ----------→ | Decrease in entropy |

Random complexity + Structuring Information ----→ | Organized complexity |

- -
- Conservation of the energy
- -
- Spontaneous evolution of a closed system if its free energy decreases
- -
- Any irreversible transformation is accompanied by an increase in entropy.

## Application to the biosphere

- Net energy input into the biosphere : 119 000 TW
- Entropy production : around 500 TW/K 1
- Energy consumption by living organisms : 95 TW

_{A}.ln(x

_{A})+x

_{B}.ln(x

_{B})]

_{A}and x

_{B}being the molar fractions of A and B in the mixture made up of a total of n moles.

_{A}.ln(x

_{A})+x

_{B}.ln(x

_{B})]

_{A}and X

_{B}. This is relatively easy for an observer with instruments such as a gas chromatograph or a mass spectrometer. However, achieving this aim requires knowing the identities of the A and B species, a qualitative information relative to the mixture.

^{2}of the surface of the earth [17]. If this process is considered as a thermal engine working between the temperatures of the surface of the globe (around 300K) and that of the high atmosphere (around 250K), we can calculate a maximum yield of 17%. It may therefore be deduced that the thus generated mechanical energy (17 W/m

^{2}) corresponds to a production of negentropy of 17/300 W/K.m

^{2}, or for the whole globe, approximately 29 TW/K. However, we must note that this mechanical energy will eventually be degraded into heat and dissipated in the form of infrared radiation.

## Chemical reactions

- r: rate of a simple reaction of the type A→B or A+B→C
- α: a term bringing in the concentrations of the reagent(s)
- ∆G* : variation in the free energy of the reactive molecules (J/molecule.K).
- k : kinetic constant
- k
_{B}: Boltzman's constant - T: Temperature at which the reaction takes place (K)

- ∆H* being the enthalpy of activation expressed in J/mol.K
- ∆S* being the entropy of activation expressed in J/mol.K
- R : constant of perfect gases = 8.31 J/mol.K

_{A+B}being the kinetic constant for reaction A+B→C

- -
- By stabilizing the transition state,
- -
- By holding the reactants in close proximity,
- -
- By holding the reactants in the right configuration to react,
- -
- By blocking side reactions,
- -
- By stretching bonds to make them easier to break.

## Extensions to other area

_{2}O, CO

_{2}, CH

_{4}, NH

_{3}, etc..) present in the gaseous atmosphere or dissolved in the oceans were adsorbed on the surface of minerals. Next, various catalytic reactions produced more complex molecules, used as precursors for obtaining the chemical functions necessary for life (amino-acids, sugars, fatty acids, etc.).

- •
- Solid catalysts [6]: crystalline structure, electric charge distributed on atoms at the surface, electron mobility, etc.
- •
- Homogeneous catalysts [18]: anions or cations possessing one or several electric charges, hydrogen bond, electronic density distribution in the various molecular orbitals, etc.
- •
- Enzymes: the same as for the homogeneous catalysts, but with the spatial distribution of the active groups being of greater importance [11].

^{3}=64 words, a figure much greater than 20, the number of amino-acids to be selected during the synthesis of proteins. We must underline the enormous amount of information stored by the DNA that, in human beings, contains about 75000 genes, each gene requiring between 2000 and 5000 bases, without counting intergenic zones that account for more than 70% of the DNA.

## Conclusion

## References

- Brillouin, L. La science et la théorie de l'information; Masson: Paris, 1959. [Google Scholar]
- Atlan, H. L'organisation biologique et la théorie de l'information; Herman, Editeurs des Sciences et des Arts: Paris, 1992. [Google Scholar]
- Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 22, 379–423; 636–656. [Google Scholar] [CrossRef] - Tonnelat, J. Thermodynamique Probabiliste: un refus des dogmes; Editions Masson: Paris, 1991. [Google Scholar]
- Delahaye, J.-P. Information, complexité et hasard; Editions Hermes: Paris, 1994. [Google Scholar]
- Masel, R.I. Chemical Kinetics and Catalysis; Wiley Interscience editor, 2001. [Google Scholar]
- Wolfenden, R.; Snider, M.J. The depth of chemical time and the power of enzymes as catalysts. Acc. Chem. Res.
**2001**, 34, 938–945. [Google Scholar] [CrossRef] [PubMed] - Stajbl, Marek and al. Calculations of activation entropies of chemical reactions in solution. J. Phys. Chem. B
**2000**, 104(18), 4578–4584. [Google Scholar] Ab Initio evaluation of the free energy surfaces for the general base/acid catalysed hydrolysis. J. Phys. Chem., B**2001**, 105(19), 4471–4484. [CrossRef] - Nevecna, T. and al. A study of effects of temperature and medium on reaction of trimethylamine with ethyl bromide. Collect. Czech. Chem. Commun.
**1994**, Vol.59, 1384–1391. [Google Scholar] [CrossRef] - Monod, J. Le hasard et la nécessité; Editions du Seuil: Paris, 1970. [Google Scholar]
- Copeland, R.A. Enzymes; Wiley VCH editor, 2000. [Google Scholar]
- Roederer, J.G. On the concept of information and its role in nature. Entropy
**2003**, 5, 3–33. [Google Scholar] [CrossRef] Information and its role in nature; Springer-Verlag: Berlin, 2005. - Wang, D.Z. Conservation of helical asymmetry in chiral interactions. CPS :orgchem/0403001; 2004. [Google Scholar]
- Barteri, M.; Pispisa, B. Coupling between binding-induced conformational phenomena: stereospecific effects in asymmetric reactions. J. Chem. Soc. Faraday Trans. 1
**1982**, 78, 2073–2084. [Google Scholar] [CrossRef] - Maurel, M.-C. Les origines de la vie; Editions Syros: Paris, 1994. [Google Scholar]
- Smith, J.M.; Szathmary, E. The origins of life; Oxford University Press, 1994. [Google Scholar]
- I.P.C.C. Climate change 2001: The scientific basis; Cambridge University Press, 2001. [Google Scholar]
- Bhaduri, S.; Mukesh, D. Homogeneous Catalysis: Mechanism and industrial applications; Wiley-Interscience, 2000. [Google Scholar]
- Rosen, M.A.; Scott, D.S. Entropy production and exergy destruction: Part I. International Journal of Hydrogen Energy
**2003**, 28, 1307–1313. [Google Scholar] [CrossRef] - Gouverneur, V.; Reiter, M. Advances in Organic Chemistry; Atta-ur-Rahman, Ed.; Bentham Science Publishers, 2005; Vol.1, pp. 519–540. [Google Scholar]
- Néda, Z.; et al. The sound of many hands clapping. Nature
**2000**, Vol. 403, 849–850. [Google Scholar] [PubMed] - Ayres, R.T. Information, entropy and progress: a new evolutionnary paradigm; American Institute of Physics Press, 1994. [Google Scholar]
- Schneider, T.D. New approaches in mathematical biology: Information theory and molecular machines. In Chemical Evolution: Physics of the Origin and Evolution of Life; pp. 313–321. Kluwer Academic Publishers: The Netherlands, 1996. [Google Scholar]
- Takahiro, T.; et al. Chiral perturbation factor approach reveals importance of entropy. J. Org. Chem.
**2002**, 67, 6593–6598. [Google Scholar] - Serizawa, T.; et al. Polymerization within a molecular-scale stereo-regular template. Nature
**2004**, (6 May). Vol.429, 52–55. [Google Scholar] [CrossRef] [PubMed] - Dill, K.A. Additivity principles in biochemistry. Journal of Biological Chemistry
**1997**, Vol.272, N°2. 701–704. [Google Scholar] [CrossRef] [Green Version] - Chaisson, Eric, J. Cosmic evolution: The rise of complexity in Nature; Harvard University Press, 2001. [Google Scholar]
- Hazen, Robert, M. Gen.e.sis : The scientific quest for life’s origin; Joseph Henry Press: Washington, 2005. [Google Scholar]
- Loewenstein, Werner, R. The touchstone of Life; Oxford University Press, 1999. [Google Scholar]
- Vidal, Jean. Thermodynamics. Editions Technip: Paris, 2003. [Google Scholar]
- Wächterhäuser, G. Life as we don’t know it. Science
**2000**, Vol.289, 1307–1308. [Google Scholar]

^{1}TW/K= 10^{12}Watt/°Kelvin , with a reference environment temperature of the earth of 282 K

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**MDPI and ACS Style**

Trambouze, P.J. Structuring Information and Entropy: Catalyst as Information Carrier. *Entropy* **2006**, *8*, 113-130.
https://doi.org/10.3390/e8030113

**AMA Style**

Trambouze PJ. Structuring Information and Entropy: Catalyst as Information Carrier. *Entropy*. 2006; 8(3):113-130.
https://doi.org/10.3390/e8030113

**Chicago/Turabian Style**

Trambouze, Pierre J. 2006. "Structuring Information and Entropy: Catalyst as Information Carrier" *Entropy* 8, no. 3: 113-130.
https://doi.org/10.3390/e8030113