Fractal Structures form Spontaneously due to Nature’s Drive to Augment Entropy Production

Increasing evidence suggests that the physical drive for maximal entropy production is responsible for spontaneous formation of fractal multi-scale self-similar structures in time and space, ubiquitous and essential for health. Fractal structures spontaneously form in nature because it is the most efficient way to optimize entropy production. Moreover it is hypothesized that the evolutionary drive for enhanced function and adaptability selects states with both robust basal and maximal entropy production (i.e. the capacity to augment it when required). Based on these premises we postulate that 1) alterations in physiologic and anatomic fractal structures may be an early indicator of illness and disease and 2) enhancing a patient’s basal and maximal entropy production will improve their health.

Understanding how nature drives entropy production offers novel insights regarding patient

care. While energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible.The Maximum Entropy Production Principle (MEPP) states that a complex non-equilibrium system will adopt an internal state of greater complexity (i.e. complex order) if the state is associated with greater energy flow, which enables greater energy gradient dissipation, and thus greater entropy production; that is, ordered structures form to enhance energy flows. 79  Examples are replete in nature, from Bénard cells (i.e., the spontaneous appearance of currents in liquid layers to enhance energy dissipation) and the spontaneous formation of a whirlpool that enhances the flow down the drain of a bathtub, to tornados, hurricanes, and more.

According to MEPP, the origin of the complexity of oxygen burning metabolism has arisen from the dynamics of living systems adjusting themselves to lead to maximum entropy production. 80 In addition to metabolic function, MEPP may be the reason why characteristic physiologic structures over time and space form spontaneously. Specifically, the ubiquitous presence of fractal structures (i.e. demonstrate multi-scale self-similarity) are hypothesized to originate because they optimize entropy production. Spatially, alterations in these fractal structures are associated with systemic change, known as illness in patients (e.g. altered tracheobronchial tree structure in asthma, 81,82, altered vasculature in stroke 83,84 and altered CNS fractal dimensions in brain pathology 85). Temporally, nature is also replete with complex time-series, which display power-law dynamics, again with bounded multi-scale self-similarity, These characteristics are found with heart rate variability (HRV) and respiratory rate variability (RRV), and whose complexity characteristics are preserved in health, and reduced with illness, stress and ageing. There are numerous techniques to measure variability 6,35,86,87 and which have demonstrated that altered HRV is associated with renal failure 88,89, heart failure 90,91, angina 92, diabetes 93, hypertension 94, myocardial infarction 95,96, coronary artery disease 97, infection 23,24,98, organ failure 27, respiratory illness 28, and extubation outcomes; 29,33 while reduced RRV is associated with organ failure 27and restrictive lung disease.28, increased stress during weaning from mechanical ventilation.29-31 and is predictive of extubation failure.32,33

Regarding the impact of evolution and maximum entropy production on human health, it is hypothesized that while nature’s physical efforts serve to augment entropy production, complexity and function, evolution selects for adaptability or ability to tolerate increased workload, measurable by the capacity to augment entropy production if and when required. Both function and adaptability, measured by basal and maximal entropy production, are thus hypothesized to be a useful means to measure health. Basal entropy production is necessary for function, maintenance and repair (i.e. healing), yet capacity to augment entropy production and augment work output would be required for adaptability, capacity to augment workload, to evade or respond to threats, either physical or illness related. Illness is thus hypothesized to be characterized by reduction in either resting and/or maximal entropy production thought to be reflected by a reduction in resting energy expenditure or maximal oxygen consumption or both; however, if the reduction in maximal consumption is profound, then there is a compensatory elevation in resting energy expenditure, for example with COPD 99 or sepsis 100.

The MEPP highlights nature’s drive for non-equilibrium systems to augment their entropy production if possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. Both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to stress and illness. With the implications of developing a novel understanding of health, illness, and treatment strategies we hypothesize that a targeted focus on optimizing our patients’ entropy production has the potential to improve both patient health and clinical outcomes.

Relevant Papers:

  1. Seely AJE Optimizing Our Patients’ Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology Entropy 2020, 22, 1095.
  2. Seely AJE, Newman K, Herry, C. Fractal Structure and Entropy Production within the Central Nervous System. Entropy 2014, 16(8): 4497-4520.
  3. Sturmberg JP, Bennett JM, Picard M, Seely AJE. The trajectory of life. Decreasing physiological network complexity through changing fractal patterns. Front Physiol. 2015, Jun 2;6:169. eCollection 2015.
  4. Seely AJE, Macklem P.  Fractal variability: An emergent property of complex dissipative systems.  Chaos. 2012 Mar;22(1):013108
  5. Macklem P, Seely AJE. Towards a Definition of Life, Perspective in Biology and Medicine 2010, 53(3):330.
  6. Seely AJE. Life,emergence and entropy production (invited commentary). J Appl Physiol. 2008 Jun;104(6):1850.

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