Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis

Driven anomalous diffusions (such as those occurring in some surface growths) are currently described through the nonlinear Fokker-Planck-like equation (∂/∂t)p^μ=-(∂/∂x)[F(x)p^μ]+D(∂²/∂x² )p^ν [(μ,ν)∈R² F(x)=k₁-k₂x is the external force; k₂>=0]. We exhibit here the (physically relevant) exact solution for all (x,t). This solution was found through an ansatz based on the generalized entropic form S_q[p]=\{1-∫du[p(u)]^q\}/(q-1) (with q∈R), in a completely analogous manner through which the usual entropy S₁[p]=-∫dup(u)lnp(u) is known to provide the correct ansatz for exactly solving the standard Fokker-Planck equation (μ=ν=1). This remarkably simple unification of normal diffusion (q=1), superdiffusion (q>1) and subdiffusion (q<1) occurs with q=1+μ-ν.