## THERMAL SCIENCE

International Scientific Journal

retracted

### RESEARCH IN ENTROPY WONTERLAND: A REVIEW OF THE ENTROPY CONCEPT

**ABSTRACT**

The entropy concept was introduced in the mid-nineteenth century by Clausius and has been continually enriched, developed and interpreted by researchers in many scientific disciplines. The use of entropy in a wide range of fields has led to inconsistencies in its application and interpretation, as summarized by von Neuman “No one knows what entropy really is.” To resolve this problem, thermodynamics and other scientific disciplines face several crucial questions concerning the entropy concept: (1) What is the physical meaning of entropy? (2) Is entropy a subjective or an objective property? (3) How to apply entropy to living organisms? To answer these questions, this paper describes the roots, the conceptual history of this important concept, as well as the path of development and application in various scientific disciplines, including classical thermodynamics, nonequilibrium thermodynamics, statistical mechanics and life sciences.

**KEYWORDS**

PAPER SUBMITTED: 2018-01-15

PAPER REVISED: 2018-01-21

PAPER ACCEPTED: 2018-01-23

PUBLISHED ONLINE: 2018-02-18

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**2**, PAGES [1163 - 1178]

- Clausius, R., On different forms of the fundamental equations of the mechanical theory of heat and their convenience for application, in The second law of thermodynamics, (Ed. J. Kestin), Dowen, Hutchingson and Ross, Inc., Stroudsburg, PA, 1976
- Edington, A.S., The nature of the physical world, Cambridge University Press, Cambridge, UK, 1928
- Schlipp, P.A., Albert Einstein: Philosopher-Scientist, Open Court Publishing, La Salle, IL, 1973
- Atkins, P., de Paula, J., Physical Chemistry, 8th ed., W.H. Freeman and Company, New York, NY, 2006
- Demirel, Y., Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, 3rd ed., Elsevier, Amsterdam, Netherlands, 2014
- Sandler, S. I., An Introduction Applied to Statistical Thermodynamics, John Wiley & Sons, NJ, 2011
- McQuarrie, D.A., Statistical Mechanics, University Science Books, Sausalito, CA, 2000
- Dugdale, J.S., Entropy and its Physical Meaning, Taylor & Francis Ltd, London, UK, 1996
- Goldstein, S., Lebowitz, J.L., On the (Boltzmann) Entropy of Nonequilibrium Systems, arXiv, (2003), arXiv:cond-mat/0304251
- Liddle, A., An introduction to modern cosmology, 2nd ed., Wiley, Chichester, UK, 2003
- Gems, D., Doonan, R., Antioxidant defense and aging in C. elegans, Is the oxidative damage theory of aging wrong?, Cell Cycle, 8 (2009), 11, pp. 1681-1687
- Hayflick, L., Entropy explains aging, genetic determinism explains longevity, and undefined terminology explains misunderstanding both, PLoS Genet., 3 (2007), 12, pp. 2351-2354
- Hayflick, L., How and why we age, Experimental Gerontology, 33 (1998), 7-8, pp. 639-653
- Hayflick, L., Biological aging is no longer an unsolved problem, Annals of the New York Academy of Sciences, 1100 (2007), pp.1-13, DOI: 10.1196/annals.1395.001
- Silva, C., Annamalai, K., Entropy generation and human ageing: Lifespan entropy and effect of physical activity level, Entropy, 10 (2008), pp. 100-123
- Atkins, P., De Paula, J., Physical chemistry for the life sciences, W.H. Freeman and Company, New York, NY, 2006.
- Rong, Q., Entropy-Based Set Pair Analysis Model on Geological Disaster Risk for Military Engineering, Engineering, 4 (2012), pp. 76-82
- Rosenfeld, R., Adaptive Statistical Language Modeling: A Maximum Entropy Approach, Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA, 1994, www.cs.cmu.edu/~roni/papers/me-thesis-TR-94-138.pdf
- Kovalev, A.,(2015) Misuse of Thermodynamic Entropy in Economics, Energy, 100 (2016), pp. 129-136, DOI: 10.1016/j.energy.2016.01.071
- Gabriel, A., Hotelling role for entropy-constrained economic growth, Ecological economics, 133 (2017), 1, pp. 35-41
- Shannon, C., A mathematical theory of communication, The Bell System Technical Journal, 27 (1948), pp. 379-423
- Kostic, M.M., The Elusive Nature of Entropy and Its Physical Meaning, Entropy, 16 (2014), pp. 953-967
- Ben-Naim, A., Discover Entropy and the Second Law of Thermodynamics: a Playful Way of Discovering a Law of Nature, World Scientific, Singapore, Singapore, 2012
- Tribus, M., McIrving, E. C., Energy and Information, Scientific American, 225 (1971), pp. 179-88
- Gillet, S., Entropy and its misuse, I. Energy, free and otherwise. Ecological Economics, 56 (2006), 1, pp. 58-70
- Choe, G.H., Stochastic Analysis for Finance with Simulations; Springer, Berlin, Germany, 2016 (page 583)
- Kozliak, E., Lambert, F., Residual Entropy, the Third Law and Latent Heat, Entropy, 10 (2008), pp. 274-284
- Denbigh, K.G., Denbigh, J.S., Entropy in relation to incomplete knowledge, Cambridge university press, Cambridge, UK, 1985.
- Jaynes, E.T., Information theory and statistical mechanics. Phys. Rev., 106 (1957), pp. 620-630
- Ben-Naim, A., Casadei, D., Modern thermodynamics, World Scientific, Singapore, Singapore, 2016.
- Singh, V., Fiorentino, M., Entropy and Energy Dissipation in Water Resources, Springer-Science, Berlin, Germany, 1992.
- Bohm, D., Peat, D., Science, Order, and Creativity, Routledge, London, 2000 (page 139)
- Bunge, M., Epistemology & Methodology III: Philosophy of Science and Technology Part I, Springer, Berlin, Germany, 1985
- Hintikka, J., Rudolf Carnap, Logical Empiricist: Materials and Perspectives, Springer, Berlin, Germany, 1975
- Schrödinger, E., What is life? The physical aspect of the living cell, 10th printing, Cambridge university press, Cambridge, UK, 2003
- Mahulikar, S.P., Herwig, H., Exact thermodynamic principles for dynamic order existence and evolution in chaos, Chaos, Solitons & Fractals, 41 (2009), 4, pp. 1939-1948
- Davis, P., Rieper, E., (2013)., Self-organization and entropy reduction in a living cell, BioSystems, 111 (2013), pp. 1-10
- Ho, M.W., What is (Schrödinger's) Negentropy?, Modern Trends in BioThermoKinetics, 3 (1994), pp. 50-61
- Ho, M.W., The Rainbow and the Worm: The Physics of Organisms, World Scientific, Singapore, Singapore, 1998
- Hansen, L., Criddle, R.S., Battley, E.H., Biological calorimetry and the thermodynamics of the origination and evolution of life, Pure Appl. Chem., 81 (2009), 10, pp. 1843-1855
- Hansen, L., Criddle, R.S., Battley, E.H., Equilibrium thermodynamics and metabolic Calorimetry of living systems, Proceedings, 20th ICCT, Warsaw, Poland, 2008, Vol 1
- Popovic, M., Entropy change of open thermodynamic systems in self-organizing processes, Thermal Science, 18 (2014), 4, pp. 1425-1432
- Münster, A., Classical Thermodynamics, Wiley-Interscience, London, UK, 1970
- Sears, W., Salinger, L., Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, 3rd ed., Addison-Wesley, Boston, MA, 1986
- Lucia, U., Probability, ergodicity, irreversibility and dynamical systems, Proceedings of the Royal Society A, 464 (2008), pp. 1089-1104
- Müller, I., A History of Thermodynamics: The Doctrine of Energy and Entropy, Springer, Berlin, Germany, 2007
- Carnot, S., Reflections on the Motive Power of Fire, Chapman &Hall ltd., London, UK, 1897
- Clausius, R., The Mechanical Theory of Heat - with its Applications to the Steam Engine and to Physical Properties of Bodies, John van Voorst, London, UK, 1867
- Clausius, R., On a Mechanical Theorem Applicable to Heat, Philosophical Magazine Series 4, 40 (1870), 265, pp. 122-127
- Balmer, R.T., Modern Engineering Thermodynamics, Academic Press, Cambridge, MA, 2011
- Gibbs, J.W., A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Transactions of the Connecticut Academy of Sciences, (1873), pp. 382-404.
- Von Helmholtz, H Physical memoirs; Taylor and Francis: London, UK, 1888.
- Glansdorff, P., Prigogine, I., Thermodynamic theory of structure, stability and fluctuations. Wiley-Interscience, New York, NY, 1971
- Popovic, M., Living organisms from Prigogine's perspective: an opportunity to introduce students to biological entropy balance, Journal of Biological Education, (2017), DOI: dx.doi.org/10.1080/00219266.2017.1357649
- Demirel, Y., Nonequilibrium thermodynamics modeling of coupled biochemical cycles in living cells, Journal of Non-Newtonian Fluid Mechanics, 165 (2010), 17-18, pp. 953-972
- von Bertalanffy, L., The theory of open systems in physics and biology, Science, 111 (1950), pp. 23-29
- Belof, J., Derivation of the Partition Function for Generalized Ensembles, arXiv, (2013), DOI: arxiv.org/abs/1309.2017v1
- Boltzmann, L., The second law of thermodynamics, in Theoretical physics and philosophical problems, (Ed. B.F. McGuinness), Springer-Verlag, New York, NY, 1974
- Morowitz, H.J., Energy flow in biology; Academic Press, New York, NY, 1968
- Brillouin, L., Maxwell's Demon Cannot Operate: Information and Entropy I. J. Appl. Phys., 22 (1951), pp. 334-337
- Caggio, V., Negentropy Meaning and New Meaning, Nuove Accezioni, Lulu press, Morriswille, NC, 2007
- Magalhães, G., (2015), Some Reflections on Life and Physics: Negentropy and Eurhythmy, Quantum Matter, 4 (2015), 3, pp. 258-266
- Brillouin, L., Negentropy and Information in Telecommunications, J. Appl. Phys., 25 (1954), pp. 595
- Garby, L., Larsen, P. S., Bioenergetics; Cambridge University Press, Cambridge, UK, 1995
- Gladyshev, G., Thermodynamic Theory of Biological Evolution and Aging, Entropy, 1 (1999), 4, pp. 55-68
- Kozliak, E., Consistent Application of the Boltzmann Distribution to Residual Entropy in Crystals, J Chem. Educ., 84 (2007), pp. 493-498
- Popovic, M., Are Shannon entropy and Residual entropy synonyms?, Proceedings, 2nd Int. Electron. Conf. Entropy Appl., Sciforum Electronic Conference Series, 2015, Vol. 2, pp. A004, DOI: 10.3390/ecea-2-A004
- Clayton, J., Giauque, W., The Heat Capacity and Entropy of Carbon Monoxide, J. Am. Chem. Soc., 54 (1932), pp. 2610-2626
- Johari, G., Configurational and residual entropies of nonergodic crystals and the entropy's behavior on glass formation, The Journal of Chemical Physics, 132(2010), pp. 124509, DOI:10.1063/1.3364999
- Sestak, J., Mares, J., Hubik, P., Glassy, Amorphous and Nano-Crystalline Materials: Thermal Physics, Analysis, Structure and Properties, Springer, Berlin, Germany, 2011
- Pauling, L., The structure and entropy of ice and of other crystals with some randomness of atomic arrangement, J.Am.Chem.Soc., 57 (1935), 12, pp. 2680-2684
- Gibson, G.E., Giauque, W.F., The third law of thermodynamics. Evidence from the specific heats of glycerol that the entropy of a glass exceeds that of a crystal at the absolute zero, J.Am.Chem.Soc., 45 (192)3, 1, pp. 93-104
- Pinal, R., Effect of molecular symmetry on melting temperature and solubility, Org. Biomol. Chem., 2 (2004), 18, pp. 2692-2699
- Boltzmann, L., Lectures on gas theory, Dover Publications, Mineola, NY, 1995. (English translation of: Boltzmann, L. Vorlesungen über gastheorie, J.A. Bath, Leipzig, Germany, 1896)
- Gibbs, J.W., Elementary principles in statistical mechanics, Yale University Press, New Haven, CT, 1902
- Popovic, M., Comparative study of entropy and information change in closed and open thermodynamic systems, Thermochimica acta, 598 (2014), pp. 77-81, DOI: 10.1016/j.tca.2014.11.002