The arrow of time (second law) as a randomness-driven emergent property of large systems

TL;DR

This paper demonstrates through simulations that the arrow of time emerges as a consequence of large system size and randomness, with recurrence times varying among particle types and distributions.

Contribution

It introduces a probabilistic framework to explain the arrow of time as an emergent property in large systems, providing explicit recurrence time expressions for different particle types.

Findings

Recurrence time grows rapidly with system size.

Bosons have the shortest recurrence time, classical particles the longest.

Distribution of recurrence times is Poisson for Bosons, Gaussian for Fermions and classical particles.

Abstract

The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of nanotechnology and associated experimental techniques has brought the arrow of time at the forefront because of its practical implications. Using simulations of one-dimensional diffusion of a system of particles, we show that the arrow of time is an emergent property of a large system. We show that the recurrence time for a system of particles to return to its original configuration grows rapidly as the number of particles grows. Based on the simulations, we have provided the expressions for recurrence times for classical particles, Fermions, and Bosons. A system of Bosons has the shortest recurrence time, whereas a system of classical particles has the longest recurrence time. The underlying distribution around the mean recurrence time is Poisson-distributed for Bosons and Gaussian-distributed for Fermions and classical particles. The probabilistic approach to encode dynamics enables testing processes other than diffusion and quantify their effects on the recurrence time.