The convenience of a new thermodynamic frame for the description of anomalous diffusion is explored. Our research, which makes use of a recent new definition for entropy arising from multifractal analysis, shows that both dynamical and thermodynamical effects may contribute to non-classical diffusion.

https://iopscience.iop.org/article/10.1088/0305-4470/29/15/007/pdf

Non-equilibrium thermodynamics and anomalous diffusion

Introduction to Thermodynamics of Irreversible Processes.

The problem of origination of molecular asymmetry in biochemical evolution is discussed. The theoretical analysis shows that chiral purity of biomolecules has the biological significance for self-reproduction of organisms. The models of spontaneous symmetry-breaking in molecular systems are given. The aspects of various stages of biochemical evolution associated with the development of chiral polarization are analysed.

Mirror symmetry breaking in biochemical evolution

A new critical point on the stress-strain curve: Delineation of dynamic recrystallization from grain growth

Uncertainty management in dynamical systems is receiving attention in artificial intelligence, particularly in the fields of qualitative and model based reasoning. Fuzzy dynamical systems occupy a very important position in the class of uncertain systems. It is well established that the fuzzy dynamical systems represented by a set of fuzzy differential inclusions (FDI) are very convenient tools for modeling and simulation of various uncertain systems. In this paper, we discuss about the mathematical modeling of two very complex natural phenomena by means of FDIs. One of them belongs to the atmospheric cybernetics (the term has been used in a broad sense) of the genesis of a cyclonic storm (cyclogenesis), and the other belongs to the bio-medical cybernetics of the evolution of tumor in a human body. Since a discussion of the former already appears in a previous paper by the first author, here, we present very briefly a theoretical formalism of cyclone formation. On the other hand, we treat the latter system more elaborately. We solve the FDIs with the help of an algorithm developed in this paper to numerically simulate the mathematical models. From the simulation results thus obtained, we have drawn a number of interesting conclusions, which have been verified, and this vindicates the validity of our models.

/pdf/fuzzy-differential-inclusions-in-atmospheric-and-medical-4kt0mth83i.pdf

Fuzzy differential inclusions in atmospheric and medical cybernetics

The development of the thermodynamics of irreversible processes is outlined with a review of recent work and a discussion of the application of these concepts to physicochemical, biological and hydrodynamic phenomena. The extension of local thermodynamics to include a theory of stability and of fluctuations receives attention. The author concludes with remarks on the stability properties of chemical reactions in open systems and comments on the possible implications of results in the interpretation of fundamental biological phenomena.

/pdf/thermodynamic-theory-of-stability-structure-and-fluctuations-5980j2md6k.pdf

Grégoire Nicolis

Papers

Thermodynamic theory of stability, structure and fluctuations