Transient fractality as a mechanism for emergent irreversibility in chaotic Hamiltonian dynamics

TL;DR

This paper reveals that transient fractal structures in phase space can explain emergent irreversibility in reversible Hamiltonian systems, bridging the gap between microreversible laws and macroscopic irreversibility.

Contribution

It demonstrates the emergence of transient fractality in conservative Hamiltonian systems, providing a new mechanism for irreversibility based on fractal scaling and information theory.

Findings

Transient fractality appears over intermediate length scales.

Irreversibility can be quantified using information theory and fluctuation theorem.

The mechanism applies to both dissipative and conservative reversible systems.

Abstract

Understanding irreversibility in macrophysics from reversible microphysics has been the holy grail in statistical physics ever since the mid-19th century. Here the central question concerns the arrow of time, which boils down to deriving macroscopic emergent irreversibility from microscopic reversible equations of motion. As suggested by Boltzmann, this irreversibility amounts to improbability (rather than impossibility) of the second-law-violating events. Later studies suggest that this improbability arises from a fractal attractor which is dynamically generated in phase space in reversible dissipative systems. However, the same mechanism seems inapplicable to reversible conservative systems, since a zero-volume fractal attractor is incompatible with the nonzero phase-space volume, which is a constant of motion due to the Liouville theorem. Here we demonstrate that in a Hamiltonian system the fractal scaling emerges transiently over an intermediate length scale. Notably, this transient fractality is unveiled by invoking the Loschmidt demon with an imperfect accuracy. Moreover, we show that irreversibility from the fractality can be evaluated by means of information theory and the fluctuation theorem. The fractality provides a unified understanding of emergent irreversibility over an intermediate time scale regardless of whether the underlying reversible dynamics is dissipative or conservative.