Entropy as a Geometric Consequence of Higher Dimensions

Entropy has traditionally been understood as a phenomenological principle, capturing time irreversibility in physical processes. In this work, we propose that entropy can emerge as a geometric property of higher-dimensional spacetime. Within a Kaluza–Klein framework featuring an additional circular dimension proportional to particle wavelength, trajectories acquire statistical multiplicity, which naturally produces a monotonic increase in entropy and offers a geometric foundation for the second law of thermodynamics. In the broader context, we note that the association between entropy and geometry is not unprecedented: Bekenstein and Hawking showed that black holes yields entropy proportional to the horizon area. Our contribution, however, is independent of that line of research and focuses on higher-dimensional spacetime. Importantly, the framework yields concrete predictions. In the arrival-time experiment of Das and Dürr, our model uniquely predicts symmetric probability distributions when the initial state is symmetric, in contrast to the non-symmetric outcomes expected from both standard quantum and Bohmian mechanics. This provides a distinctive and testable signature for hidden dimensions.