Nonlinear Fokkerxe2x80x93Planck Equation Approach to Systems of Interacting Particles: Thermostatistical Features Related to the Range of the Interactions Nonlinear Fokkerxe2x80x93Planck equations (NLFPEs) constitute useful effective descriptions of some interacting manybody systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the     S q     powerlaw entropic functionals. Most applications of the connection between the NLFPE and the     S q     entropies have focused on systems interacting through shortrange forces. In the present contribution we revisit the NLFPE approach to interacting systems in order to clarify the role played by the range of the interactions, and to explore the possibility of developing similar treatments for systems with longrange interactions, such as those corresponding to Newtonian gravitation. In particular, we consider a system of particles interacting via forces following the inverse square law and performing overdamped motion, that is described by a density obeying an integrodifferential evolution equation that admits exact timedependent solutions of the qGaussian form. These qGaussian solutions, which constitute a signature of     S q    thermostatistics, evolve in a similar but not identical way to the solutions of an appropriate nonlinear, powerlaw Fokkerxe2x80x93Planck equation.

In pursuit of the framework behind the biosphere: Scurves, selfassembly and the genetic entropy paradox Abstract   The origins, evolution and functioning of the Biosphere have occupied humankind for as long as recorded history has existed. In this paper we examine the claims of thermodynamics to be the framework within which we can understand the evolution, functioning and development of the Biosphere, exploring the evidence from ecology, molecular science and evolutionary biology, and particularly focussing upon the maximum entropy production principle (MEPP), and its explanatory potential in terms of many of the logistic relationships found within the Biosphere. We introduce the genetic entropy paradox, where the DNA increases in terms of internal information entropy, as the genetic code is continuously randomized through mutation, and yet this leads to increasing external entropy production, as increasingly more complicated structures and functions are produced in the form of new protein morphologies and metabolic pathways (again determined by the bioenergetic context). We suggest that the central dogma acts as a form of entropy exchange mechanism, but at the core of this is change in information entropy, which increases within the genetic code, and decreases within the organism. This would appear to be a truly unique event, and highlights a key interaction between two levels of organization within the Biosphere, the genome and the proteome, in terms of entropy production. The Biosphere is seen as being composed of a series of selforganizing subgroups, each maximizing entropy production within the constraints of time, feedback and system constraints. The entropic production of the Biosphere is thus an emergent property.