Up-Hill Diffusion Creating Density Gradient - What is the Proper Entropy?

Abstract

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here, we investigate a different type: the topological constraint imposed on `space'. Such constraint emerges from the null space of the Poisson operator linking energy gradient to phase space velocity, and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensamble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.

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Cited by in corpus (12)

• Microscopic models for uphill diffusion
• Stationary uphill currents in locally perturbed Zero Range Processes
• Diffusion with finite-helicity field tensor: a new mechanism of generating heterogeneity
• A Collision Operator for Describing Dissipation in Noncanonical Phase Space
• Dissipative Brackets for the Fokker-Planck Equation in Hamiltonian Systems and Characterization of Metriplectic Manifolds
• Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas
• Charged Particle Diffusion in a Magnetic Dipole Trap
• Degenerate Laplacian: A Classification by Helicity
• Maximum entropy states of collisionless positron-electron plasma in a dipole magnetic field
• Beltrami operators
• Poissonization of Three Dimensional Nonholonomic Dynamics with the Method of Extension
• Inward Diffusion and Acceleration of Particles Driven by Turbulent Fluctuations in Magnetosphere