Identifying disorder and abnormal incidents in traffic flow: a thermodynamics approach based on differential velocity entropy

Macroscopic traffic safety situation estimation is an important prerequisite for identifying abnormal incidents and ensuring the safe operation of road network. Existing traffic flow metrics fail to comprehensively quantify disorder associated with crash risks and abnormal events. Inspired by thermodynamics, this research proposes a differential velocity entropy based on the distribution of velocity vectors and the maximum entropy (ME) approach. This entropy models the disorder in traffic flow, capturing additionally information typically overlooked in traditional fundamental diagrams. As a non-parametric measure of disorder, it eliminates heterogeneity arising from bin selection and sample size effects in quantitative analysis. Numerical simulations demonstrate its sensitivity to traffic phase transitions, revealing the spatial and temporal locations of bottlenecks. Subsequently, we conducted an empirical study with the I-24 MOTION dataset to assess the metric’s ability to identify crash impacts. The results show that entropy peaks correlate spatially and temporally with accident locations, and its evolution captures the propagation range of accident’s impact. Additionally, differential velocity entropy shows a strong association with conflict frequency and can serve as a key traffic-flow indicator for identifying the macroscopic traffic safety situation.