Irreversibility from staircases in symplectic embeddings
arXiv:1806.11305 · doi:10.1016/j.physa.2018.09.047
Abstract
We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamitonian systems of many degrees of freedom. We use recent flexibility and rigidity results of symplectic embeddings, quantified via the (stabilized) Fibonacci and Pell staircases, to encode the underlying breadth of the possible initial conditions, which alongside the multitude of degrees of freeedom of the underlying system give rise to time-irreversibility.
27 pages. No figures. LaTeX2e. This version: two additional references. Accepted for publication by Physica A
References in corpus (25)
- A lecture on the classical KAM theorem
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- Phase transitions and configuration space topology
- Symplectic embeddings of 4-dimensional ellipsoids: erratum
- New obstructions to symplectic embeddings
- The world of long-range interactions: A bird's eye view
- Imprints of the Quantum World in Classical Mechanics
- Quantum Blobs
- Symplectic embeddings of polydisks
- Short Time Quantum Propagator and Bohmian Trajectories
- The "Symplectic Camel Principle" and Semiclassical Mechanics
- Symplectic embeddings of ellipsoids in dimension greater than four
- The role of the number of degrees of freedom and chaos in macroscopic irreversibility
- Symplectic embeddings of 4-dimensional ellipsoids into cubes
- Some optimal embeddings of symplectic ellipsoids
- The ghost stairs stabilize to sharp symplectic embedding obstructions
- Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs
- Tsallis entropy induced metrics and CAT(k) spaces
- Ellipsoid embeddings and symplectic packing stability
- The Hofer question on intermediate symplectic capacities
- Long-range interactions, doubling measures and Tsallis entropy
- Vanishing largest Lyapunov exponent and Tsallis entropy
- Time irreversibility from symplectic non-squeezing
- Entropies from coarse-graining: convex polytopes vs. ellipsoids
- Symplectic embeddings of 4-dimensional ellipsoids into polydiscs