Randomness Increases Order in Biological Evolution

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness

Conservation, Creation, and Evolution: Revising the Darwinian Project

There is hardly anything more central to our universe than conservation. Many scientific fields and disciplines view the law of conservation as one of the most fundamental universal laws. The Darwinian model pivots the process of evolution on variability, reproduction, and natural selection. Conservation plays a marginal role in this model and is not really universal, as the model allows exceptions to conservation, i.e. non-conservation, to play an equally important role in evolution. This anomalous role of conservation in the Darwinian model raises questions: What is the reason for this anomaly? Is conservation really universal, as we tend to believe or is it not, as the Darwinian model suggests? This contribution proposes a new model of evolution that focuses on levels of organization, rather than of species, organisms, or populations. It argues that conservation is central to evolution. Not only does this new model restores the universal status of conservation but it also makes possible to resolve some outstanding problems and controversies that continue to plague the Darwinian model. The article tries to advance the broad Darwinian project that seeks to explain the process of evolution as a product of the spontaneous processes in nature

From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity

Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes.Comment: Phylosophica

Stochastic resonance in a model of opinion formation on small-world networks

We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a ``fashion wave''. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed.Comment: 5 pages, 5 figures include

Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from Liouville's equation for Hamiltonian dynamical systems. The relaxation rates can be conceived in terms of the so-called Pollicott-Ruelle resonances. In spatially extended systems, the transport coefficients can also be obtained from the Pollicott-Ruelle resonances. The Liouvillian eigenstates associated with these resonances are in general singular and present fractal properties. The singular character of the nonequilibrium states is shown to be at the origin of the positive entropy production of nonequilibrium thermodynamics. Furthermore, large-deviation dynamical relationships are obtained which relate the transport properties to the characteristic quantities of the microscopic dynamics such as the Lyapunov exponents, the Kolmogorov-Sinai entropy per unit time, and the fractal dimensions. We show that these large-deviation dynamical relationships belong to the same family of formulas as the fluctuation theorem, as well as a new formula relating the entropy production to the difference between an entropy per unit time of Kolmogorov-Sinai type and a time-reversed entropy per unit time. The connections to the nonequilibrium work theorem and the transient fluctuation theorem are also discussed. Applications to nanosystems are described.Comment: Lecture notes for the International Summer School Fundamental Problems in Statistical Physics XI (Leuven, Belgium, September 4-17, 2005