Multidimensional arrow of time

TL;DR

This paper proposes a geometric model linking the arrow of time to the growth of multidimensional manifolds, emphasizing entropy in higher dimensions as the fundamental driver of temporal directionality.

Contribution

It introduces a novel framework connecting multidimensional geometry and entropy to explain the arrow of time, differing from traditional entropy-based cosmological models.

Findings

Arrow of time explained by growth of multidimensional volume

Entropy linked to geometric background via Bekenstein-Hawking-Wald entropy

Time's directionality persists even in vacuum conditions

Abstract

This paper investigates the influence of extra dimensions on the nature of the arrow of time. We demonstrate that the observed arrow of time can be explained by the monotonic growth of the multidimensional manifold's volume. Unlike traditional cosmological approaches based on the entropy of matter or radiation, our model identifies the primary temporal direction with the Bekenstein-Hawking-Wald entropy of the geometric background. By establishing a formal relation between the statistical weight of the multidimensional manifold and the multiplicity of causally disconnected regions, we reveal that time's directionality is driven by dominant entropy production in the higher-dimensional bulk. A key consequence of this approach is that the arrow of time remains a persistent feature for a 4D observer even in the vacuum limit. This global geometric evolution suppresses local statistical fluctuations and ensures a robust and stable entropy flow throughout the manifold.