Macroscopic Car Condensation in a Parking Garage

TL;DR

This paper models a parking garage as a phase transition point in an asymmetric exclusion process, revealing how macroscopic car accumulation and information transmission emerge near critical parameters.

Contribution

It introduces a novel phase transition framework for parking garages using asymmetric exclusion process, analyzing critical scaling and fluctuation effects.

Findings

Macroscopic car condensation occurs at critical parameters.

Number of parked cars diverges with system size as N_s^{1/2}.

Transition signals the onset of information transmission.

Abstract

An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes macroscopically occupied. The total car density $\rho_o$ and the exit probability $\alpha$ are the two control parameters. At the transition, the number of parked cars $N_p$ diverges in both cases, with the length of the road $N_s$, as $N_p\sim N_s^{y_p}$ with $y_p=1/2$. Towards the transition, the number of parked cars vanishes as $N_p\sim \epsilon^\beta$ with $\beta=1$, $\epsilon=|\alpha -\alpha^*|$ or $\epsilon=|\rho^*_o -\rho_o|$ being the distance from the transition. The transition into the normal phase represents also the onset of transmission of information through the garage. This gives rise to unusual parked car autocorrelations and car density profiles near the garage, which depend strongly on the group velocity of the fluctuations along the road.