In all spatial dimensions d, we study the static and dynamical properties of a generalized Smoluchowski equation which describes the evolution of a gas obeying a logotropic equation of state, p=Alnρ. A logotrope can be viewed as a limiting form of polytrope (p=Kργ, γ=1+1/n), with index γ=0...

We introduce a new class of Fokker–Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can account for anomalous diffusion, quantum statistics, and...

We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism first provides a unifying description of classical and...

It has been hypothesized that plankton predators sense the presence of their prey through detection of chemical signals exuded by the prey. This process is formulated using elements of existing models, tailored to correspond to the specific process under investigation. The motivation for the...

We use the Chapman–Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations...