Increasing Entropy: Heat Death or Perpetual Harmonies?

Increasing Entropy: Heat Death or Perpetual Harmonies?

R.E. Ulanowicz 

Department of Botany and Zoology, University of Florida, Gainesville, USA

University of Maryland Center for Environmental Science, Solomons, USA

30 June 2009
| Citation



Classically, the increase of entropy implies an ineluctable dissipation of energy and materials into what is known as ‘heat death’. A strictly logical take on the Boltzmann entropy reveals, however, that the measure amalgamates order with disorganization. Hence, under some nonequilibrium circumstances, the production of order becomes an inevitable feature of increasing entropy. In particular, perpetual harmonies can emerge from the collapse of nonequilibrium configurations. Data from networks of trophic interactions in real ecosystems reveal a preferred balance between dissipation and order at an approximate ratio of 1:e – a phenomenon that possibly could inform the search for sustainable systems.


autocatalysis, complexity, dissipation, dualism, ecosystems, entropy, heat death, indeterminacy, information, monism, nonequilibrium, second law, sustainability, thermodynamics


[1] Eddington, A.S., The Nature of the Physical World, Macmillan: New York, pp. 74, 1928.

[2] Carnot, S., Reflections on the Motive Power of Heat, ASME: New York, 1824 (translated 1943).

[3] Boltzmann, L., Wissenschaftliche Abhandlungen, J.A. Barth: Leipzig, 1905.

[4] Gibbs, J.W., Elementary Principles in Statistical Mechanics, Ox Bow Press: Woodbridge, Connecticut, 1901 (1981).

[5] Haught, J.F., Science and Religion: In Search of Cosmic Purpose, Georgetown University Press: Washington, DC, 2001.

[6] Schroedinger, E., What is Life?, Cambridge University Press: Cambridge, 1944.

[7] Nicolis, G. & I. Prigogine, Self-organization in nonequilibrium systems: from dissipative  structures to order through fluctuations, Wiley: New York, 1977.

[8] Kauffman, S.A., Investigations, Oxford University Press: Oxford, 2000.

[9] Jørgensen, S.E. & Mejer, H.F., Exergy as a key function in ecological models. Energy and  Ecological Modelling: Developments in Environmental Modelling, eds W.J. Mitsch, R.W. Bosserman & J.M. Klopatek, Elsevier: Amsterdam, pp. 587–590, 1981.

[10] Chaisson, E.J., Cosmic Evolution: The Rise of Complexity in Nature, Harvard University Press: Cambridge, MA, 2001.

[11] Ulanowicz, R.E., An hypothesis on the development of natural communities. J. Theor. Biol., 85, pp. 223–245, 1980. doi:10.1016/0022-5193(80)90019-3

[12] Fath, B.D., Jørgensen, S.E., Patten, B.C. & Straškraba, M., Ecosystem growth and development. Biosystems, 77, pp. 213–228, 2004. doi:10.1016/j.biosystems.2004.06.001

[13] Salthe, S.N., Meaning in nature: Placing biosemiotics within pansemiotics. Biosemiotics: Information, Codes and Signs in Living Systems, ed. M. Barbieri, Nova Science Publishers: Hauppauge, New York, pp. 207–217, 2007.

[14] Swenson, R., Emergent attractors and the law of maximum entropy production: Foundations to a theory of general evolution. Systems Research, 6, pp. 187–197, 1989.

[15] Schneider, E.D. & Sagan, D., Into the Cool: Energy Flow, Thermodynamics, and Life,  University of Chicago Press: Chicago, 2005.

[16] Schneider, E.D, & Kay, J.J., Life as a manifestation of the second law of thermodynamics. 

Mathematical and Computer Modelling, 19, pp. 25–48, 1994. doi:10.1016/0895-7177(94)90188-0 

[17] Ulanowicz, R.E., Ecology, the Ascendent Perspective, Columbia University Press: New York, 1997.

[18] Morowitz, H.J., Energy Flow in Biology, Academic Press: New York, 1968.

[19] Penrose, O., An asymmetric world. Nature, 438, pp. 919, 2005.

[20] Gibbs, J.W., Elementary Principles in Statistical Mechanics, Yale University Press: New Haven, Connecticut, 1902.

[21] Tribus, M., Thermostatics and Thermodynamics, Van Nostrand: Princeton, New Jersey, 1961.

[22] Bateson, G., Steps to an Ecology of Mind, Ballantine Books: New York, 1972.

[23] Ulanowicz, R.E., Goerner, S.J., Lietaer, B. & Gomez, R. Quantifying sustainability: resilience, efficiency and the return of information theory. Ecological Complexity, 6, pp. 27–36, 2009. doi:10.1016/j.ecocom.2008.10.005

[24] Shannon, C.E., A mathematical theory of communication. Bell System Tech. J., 27, pp. 379–423, 1948.

[25] Ulanowicz, R.E. & Norden, J.S., Symmetrical overhead in flow networks. Int. J. Syst. Sci., 1, pp. 429–437, 1990.

[26] Finn, J.T., Measures of ecosystem structure and function derived from analysis of flows. J. Theor. Biol., 56(2), pp. 363–380, 1976. doi:10.1016/S0022-5193(76)80080-X

[27] Mickulecky, D.C., Network thermodynamics In biology and ecology: an introduction. Ecosystem Theory for Biological Oceanography, eds R.E. Ulanowicz & T. Platt, Canadian Bulletin of Fisheries and Aquatic Sciences: Ottawa, Vol. 213, pp. 163–175, 1985.

[28] Peirce, C.S., The doctrine of necessity examined. The Monist, 2, pp. 321–338, 1892.

[29] Whitehead, A.N., Modes of thought, The Free Press: New York, 1938 (Paperback 1968).

[30] Popper, K.R., A World of Propensities, Thoemmes: Bristol, 1990.

[31] Kolmogorov, A.N., The local structure of turbulence in incompressible viscous fluid for very large Reynold’s numbers. Comptes rendus (Doklady) de l’Académie des Sciences de l’U.R.S.S., 30, pp. 301–305, 1941.

[32] Onsager, L., Reciprocal relations in irreversible processes. Physical Review A, 37, pp. 405–426, 1931. doi:10.1103/PhysRev.37.405

[33] Kauffman, S., At Home in the Universe: The Search for the Laws of Self-Organization and Complexity, Oxford University Press: New York, 1995.

[34] Ulanowicz, R.E., Growth & Development: Ecosystems Phenomenology, Springer-Verlag: New York, 1986.

[35] Zorach, A.C. & Ulanowicz, R.E., Quantifying the complexity of flow networks: How many roles are there? Complexity, 8(3), pp. 68–76, 2003. doi:10.1002/cplx.10075

[36] Ulanowicz, R.E., Limitations on the connectivity of ecosystem flow networks. Biological Models, eds A. Rinaldo & A. Marani, Istituto Veneto de Scienze, Lettere ed Arti: Venice, pp. 125–143, 1997.

[37] Ulanowicz, R.E., Beyond the material and the mechanical: Occam’s razor is a double-edged blade. Zygon, 30(2), pp. 249–266, 1995. doi:10.1111/j.1467-9744.1995.tb00068.x

[38] Kauffman, S.A., The Origins of Order: Self-organization and Selection in Evolution, Oxford University Press: New York, 1993.

[39] Goerner, S.J., Lietaer, B., Ulanowicz, R.E. & Gomez, R., Quantifying economic sustainability: implications for free-enterprise theory, policy and practice. Ecological Economics, in review.

[40] Matutinovic´, I., The microeconomic foundations of business cycles: from institutions to autocatalytic networks. Journal of Economic Issues, 39(4), pp. 867–898, 2005.

[41] Lietaer, B., Ulanowicz, R.E. & Goerner, S.J., Options for managing systemic bank crises,, 2008.

[42] Odum, H.T. & Odum, E.C., A Prosperous Way Down: Principles and Policies, University of Colorado Press: Boulder, Colorado, 2001.