Information theory of non-equilibrium states

Melvin M. Vopson

doi:10.59973/ipil.20

Authors

Melvin M. Vopson University of Portsmouth, School of Mathematics and Physics, Portsmouth, PO1 3HF, United Kingdom

DOI:

https://doi.org/10.59973/ipil.20

Keywords:

non-equilibrium information theory;, thermal fluctuations;, digital bits;, information entropy;, information theory

Abstract

The Shannon's information theory of equilibrium states has already underpinned fundamental progress in a diverse range of subjects such as computing, cryptography, telecommunications, physiology, linguistics, biochemical signaling, mathematics and physics. Here we undertake a brief examination of the concept of information theory of non-equilibrium states. The fundamental approach proposed here has the potential to enable new applications, research methods and long-term innovations, including the principle of extracting digital information from non-equilibrium states and the development of predictive protocols of mutation dynamics in genome sequences.

References

C.E. Shannon, A mathematical theory of communication, The Bell System Technical Journal, Vol. 27, pp. 379–423 (1948). DOI: https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

M.M. Vopson, The mass-energy-information equivalence principle, AIP Adv. 9, 095206 (2019). DOI: https://doi.org/10.1063/1.5123794

H. J. Kreuzer, Nonequilibrium Thermodynamics and Its Statistical Foundations (Oxford University Press, Oxford, 1981)

P. Zikopoulos, D. deRoos, K. Parasuraman, T. Deutsch, J. Giles, and D. Corrigan, Harness the Power of Big Data: The IBM Big Data Platform (McGraw-Hill Professional, New York, 2012), ISBN: 978-0-07180818-7.

M. M. Vopson, The information catastrophe, AIP Adv. 10, 085014 (2020). DOI: https://doi.org/10.1063/5.0019941

T.A. Reichert, D.N. Cohen, A.K.C. Wong, An application of information theory to genetic mutations and the matching of polypeptide sequences, J. Theoret. Biol. 42, 245-261 (1973). DOI: https://doi.org/10.1016/0022-5193(73)90088-X

C.Cosmi, V. Cuomo, M. Ragosta, M.F. Macchiato, Characterization of nucleotide sequences using maximum entropy techniques, J. Theoret. Biol. 147, 423-432 (1990). DOI: https://doi.org/10.1016/S0022-5193(05)80497-7

H. Herzel, W. Ebeling, A.O. Schmitt, Entropies of biosequences: The role of repeats, Phys. Rev. E 50, 5061-5071 (1994). DOI: https://doi.org/10.1103/PhysRevE.50.5061

W. Li, K. Kaneko, Long-range correlations and partial 1/f spectrum in a noncoding DNA sequence, Europhys. Lett. 17(7), 655-660 (1992). DOI: https://doi.org/10.1209/0295-5075/17/7/014

C.K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simon, H.E. Stanley, Long-range correlations in nucleotide sequences, Nature 356, 168-170 (1992). DOI: https://doi.org/10.1038/356168a0

L. Wentian, G.M. Thomas, K. Kunihiko, Understanding long-range correlations in DNA sequences, Physica D: Nonlinear Phenomena, Volume 75, Issues 1–3, 392-416 (1994) https://doi.org/10.1016/0167-2789(94)90294-1. DOI: https://doi.org/10.1016/0167-2789(94)90294-1

R. Roman-Roldan, P. Bernaola-Galván, J. Oliver, Application of information theory to DNA sequence analysis: A review, Pattern Recognition, Volume 29, Issue 7, (1996) https://doi.org/10.1016/0031-3203(95)00145-X. DOI: https://doi.org/10.1016/0031-3203(95)00145-X

A. Hariri, B. Weber, J. Olmsted III, On the validity of Shannon-information calculations for molecular biological sequences, J. Theoret. Biol. 147, 235-254 (1988). DOI: https://doi.org/10.1016/S0022-5193(05)80054-2

S. Vinga, Information theory applications for biological sequence analysis, Briefings in Bioinformatics, vol. 15 (3) 376-389 (2014). DOI: https://doi.org/10.1093/bib/bbt068

J. A. Tenreiro Machado, Shannon Entropy Analysis of the Genome Code, Mathematical Problems in Engineering, Article ID 132625 (2012) https://doi.org/10.1155/2012/132625 DOI: https://doi.org/10.1155/2012/132625

F. Fernandes, A.T. Freitas, J.S. Almeida, S. Vinga, Entropic Profiler – detection of conservation in genomes using information theory, BMC Research Notes, 2:72 (2009) doi:10.1186/1756-0500-2-72 DOI: https://doi.org/10.1186/1756-0500-2-72

J.A. Tenreiro Machado, António C. Costa, Maria Dulce Quelhas, Shannon, Rényie and Tsallis entropy analysis of DNA using phase plane, Nonlinear Analysis: Real World Applications, Volume 12, Issue 6, 3135-3144 (2011) https://doi.org/10.1016/j.nonrwa.2011.05.013. DOI: https://doi.org/10.1016/j.nonrwa.2011.05.013

A. Thomas, S. Barriere, L. Broseus, J. Brooke, C. Lorenzi, J.P. Villemin, G. Beurier, R. Sabatier, C. Reynes, A. Mancheron, W. Ritchie, GECKO is a genetic algorithm to classify and explore high throughput sequencing data, Commun. Biol. 2, 222 (2019). https://doi.org/10.1038/s42003-019-0456-9 DOI: https://doi.org/10.1038/s42003-019-0456-9

M. Vopson, S.C. Robson, A new method to study genome mutations using the information entropy, Physica A: Statistical Mechanics and its Applications, Volume 584, 126383 (2021). DOI: https://doi.org/10.1016/j.physa.2021.126383

M.M. Vopson, A Possible Information Entropic Law of Genetic Mutations. Appl. Sci. 2022, 12, 6912. https://doi.org/10.3390/app12146912 DOI: https://doi.org/10.3390/app12146912

M.M. Vopson, S. Lepadatu, The second law of information dynamics, in-press AIP Advances, vol. 12, issue 7 July (2022). DOI: https://doi.org/10.1063/5.0100358

Futuyma, D.J. Evolutionary Biology, 2nd ed.; Sinauer: Sunderland, MA, USA, 1986.