Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass

Abstract

We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space where the linear (nonlinear) character of the FPE is associated with the employed deformed linear (nonlinear) derivative. The FPE for an inhomogeneous medium with a position-dependent diffusion coefficient is equivalent to a deformed FPE within a deformed space, described by generalized derivatives, and constant diffusion coefficient. The deformed FPE is consistent with the diffusion equation for inhomogeneous media when the temperature and the mobility have the same position-dependent functional form as well as with the nonlinear Langevin approach. The deformed version of the H-theorem permits to express the Boltzmann-Gibbs entropic functional as a sum of two contributions, one from the particles and the other from the inhomogeneous medium. The formalism is illustrated with the infinite square well and the confining potential with linear drift coefficient. Connections between superstatistics and position-dependent Langevin equations are also discussed.

References in corpus (27)

• Superstatistics
• Statistical mechanics in the context of special relativity
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Generalized information and entropy measures in physics
• Generalized algebra within a nonextensive statistics
• Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Thermostatistics of overdamped motion of interacting particles
• Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
• Anomalous diffusion and Tsallis statistics in an optical lattice
• Displacement operator for quantum systems with position-dependent mass
• Group entropies, correlation laws and zeta functions
• Morse potential derived from first principles
• Superstatistical generalization of the work fluctuation theorem
• A position-dependent mass harmonic oscillator and deformed space
• Generalized space and linear momentum operators in quantum mechanics
• Fractional Fokker-Planck equation from non-singular kernel operators
• Dual Conformable Derivative: Definition, Simple Properties and Perspectives for Applications
• Quantum Confinement in Nonadditive Space with a Spatially Dependent Effective Mass for Si and Ge Quantum Wells
• Landau Quantization for an electric quadrupole moment of Position-Dependent Mass Quantum Particles interacting with Electromagnetic fields
• Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy time evolution
• A new class of entropic information measures, formal group theory and information geometry
• Importance Sampling Variance Reduction for the Fokker-Planck Rarefied Gas Particle Method
• Classical and quantum dissipation in non homogeneous environments
• Lorentzian Solitary Wave in a Generalised Nonlinear Schrödinger Equation
• Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

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• Polymer Concentration Regimes from Fractional Microrheology
• Dynamics of the Modified Emden and pseudo-Modified Emden Equations: position-dependent mass, invariance and exact solvability
• Effect of nonlocal transformations on the linearizability and exact solvability of the nonlinear generalized modified Emden type equations
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