Physics NotePublished
Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
C. Tsallis; Dirk Jan Bukman
1995
Publication details
- Authors
- C. Tsallis; Dirk Jan Bukman
- Type
- Physics Note
- Status
- Published
- Publication date
- 1995
- Description
- The optimization of the usual entropy <math>S_1[p] = -\int du \ p(u)\ \ln \ p(u)</math> under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of normal diffusions. We show here that the optimization of the generalized entropic form <math>S_q[p] = \{1-\int du [p(u)]^q\}/(q-1)</math> (with <math>q=1+\mu-\nu \in \mathcal{R}</math>) <math></math>is closely related to the calculation of the exact time-dependent solutions of a generalized, nonlinear, Fokker Planck equation, namely <math>\frac{\partial}{\partial t}\ p^{\mu} = - \frac{\partial}{\partial x} [F(x) p^{\mu}] + D \frac{\partial^2}{\partial x^2} \ p^{\nu}</math>, associated with a physically meaningful ''anomalous'' diffusion in the presence of the external force <math>F(x) = k_1-k_2x\!\,</math>. Consequently, paradigmatic types of normal <math>(q=1)\!\,</math> and anomalous <math>(q\neq 1)\!\,</math> diffusions occurring in a great variety of physical situations become unified in a single picture.
- Year
- 1995
- Number
- CBPF-NF-084/95
- Linked to a thesis
- No
- Linked to a grant
- No