Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy.
Physics Department, College of Sciences, Shiraz University, Shiraz, 71454, Iran.
Sci Rep. 2020 Mar 9;10(1):4334. doi: 10.1038/s41598-020-60744-6.
We know that maximal efficiency in physical systems is attained by reversible processes. It is then interesting to see how irreversibility affects efficiency in other systems, e.g., in a city. In this study, we focus on a cyclic process of movements (home to workplace and back to home) in a city to investigate the above question. To this end, we present a minimal model of the movements, along with plausible definitions for the efficiency and irreversibility of the process; more precisely, we take the inverse of the total travel time per number of trips for efficiency and the relative entropy of the forward and backward flow distributions for the process irreversibility. We perform numerical simulations of the model for reasonable choices of the population distribution, the mobility law, and the movement strategy. The results show that the efficiency of movements is indeed negatively correlated with the above measure of irreversibility. The structure of the network and the impact of the flows on the travel times are the main factors here that affect the time intervals of arriving to destinations and returning to origins, which are usually larger than the time interval of the departures. This in turn gives rise to diverging of the backward flows from the forward ones and results to entropy (disorder or uncertainty) production in the system. The findings of this study might be helpful in characterizing more accurately the city efficiency and in better understanding of the main working principles of these complex systems.
我们知道，物理系统的最大效率是通过可逆过程实现的。那么，了解不可逆性如何影响其他系统（例如城市）的效率就很有趣。在这项研究中，我们专注于城市中循环的运动过程（往返于家和工作场所），以研究上述问题。为此，我们提出了一个运动的最小模型，并对过程的效率和不可逆性给出了合理的定义；更准确地说，我们将每次旅行的总旅行时间除以旅行次数作为效率的倒数，将正向和反向流动分布的相对熵作为过程不可逆性的度量。我们针对人口分布、移动规律和移动策略的合理选择对模型进行了数值模拟。结果表明，运动的效率确实与上述不可逆性度量呈负相关。网络结构和流动对旅行时间的影响是影响到达目的地和返回起点的时间间隔的主要因素，这些时间间隔通常大于出发时间间隔。这反过来又导致反向流动与正向流动的偏离，并导致系统中熵（无序或不确定性）的产生。本研究的发现可能有助于更准确地描述城市效率，并更好地理解这些复杂系统的主要工作原理。
