A universal state equation of particle gases for passenger flights in United States

Flight delays have negative impacts on passengers, carriers, and airports. To reduce these unpopular influence, we need to find the statistical law of the collective behavior of passenger flights. We use a mean-field approach to analyze big data listing the departure and arrival records of all American domestic passenger flights in 20 years. We treat passenger flights as particle gases and define their dimensionless velocity, quasi-thermodynamic quantities — pressure, volume, temperature, and mole number, respectively. By introducing phenomenological parameters a and b to set up van der Waals-like state equations, we erect a universal gaseous constant R for actually operated passenger flights, their counterparts on schedule, and ”delayor gases” defined as the difference between them. We find that the attractive coefficient of ”delayor gases” positively correlates with the average delay per flight on airports. Rescaling state equations for passenger flights across all 20 years, we find a universal function. This is a significant step toward understanding flight delays and dealing with temporal big data with the tools of statistical physics.