Recovering Gardner Restacking with Purely Diffusive Operations

Abstract

The maximum particle kinetic energy that can be extracted from an initial six-dimensional phase space distribution motivates the concept of free or available energy. The free energy depends on the allowed operations that can be performed. A key concept underlying the theoretical treatment of plasmas is the Gardner free energy, where the exchange of the contents of equal phase volumes is allowed. A second free energy concept is the diffusive free energy, in which the contents of volumes are instead averaged. For any finite discretization of phase space, the diffusive free energy is known to be less than the Gardner free energy. However, despite the apparent fundamental differences between these free energies, it is demonstrated here that the Gardner free energy may be recovered from the continuous limit of the diffusive free energy, leading to the surprise that macroscopic phase-space conservation can be achieved by ostensibly entropy-producing microscopic operations.

arXiv comment8 pages, 3 figures

References in corpus (16)

• Quantum coherence, time-translation symmetry and thermodynamics
• The general structure of quantum resource theories
• Structure and structure-preserving algorithms for plasma physics
• Hamiltonian integration methods for Vlasov-Maxwell equations
• Petawatt laser absorption bounded
• Available energy and ground states of collisionless plasmas
• Avoiding irreversibility: engineering resonant conversions of quantum resources
• Coupling of alpha-channeling to parallel wavenumber upshift in lower hybrid current drive
• Available energy of magnetically confined plasmas
• Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
• Alpha Channeling with High-field Launch of Lower Hybrid Waves
• The geometric theory of charge conservation in particle-in-cell simulations
• Available Energy from Diffusive and Reversible Phase Space Rearrangements
• Maximal energy extraction under discrete diffusive exchange
• On extreme points of the diffusion polytope
• Nonequilibrium Kinetics of One-Dimensional Bose Gases

Cited by in corpus (7)

• The available energy of trapped electrons and its relation to turbulent transport
• Loss-Cone Stabilization in Rotating Mirrors: Thresholds and Thermodynamics
• Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
• Minimum Stabilizing Energy Release for Mixing Processes
• Upper and Lower Bounds on Phase-Space Rearrangements
• Majorization requires infinitely many second laws
• Approximating the Particle Distribution in Rotating and Tandem Mirror Traps