Structural Coupling Between Shannon Entropy and Dwell-Time Entropy Across Emotional and Safety-Critical Visual Tasks

This study investigated the relationship between fixation-frequency-based Shannon entropy and dwell-time-based entropy across two different visual task domains: emotional evaluation of automotive exterior designs and safety-critical monitoring of nuclear power plant emergency scenarios. Although gaze entropy has been widely used to explain emotional responses, task performance, and situation awareness, the relationship between entropy measures derived from fixation counts and fixation durations remains insufficiently examined. Eye-tracking data were analyzed from two experiments with different attentional characteristics. In the emotional visual task, 10 participants evaluated three automotive design images. In the safety-critical task, 20 participants performed four nuclear power plant emergency monitoring scenarios. Shannon entropy and dwell-time entropy were calculated using fixation count and fixation duration distributions across Areas of Interest, respectively. Pearson correlation and simple regression analyses were conducted within each task domain. The results showed strong positive associations between Shannon entropy and dwell-time entropy in both domains. The emotional task showed a correlation of r = 0.844, while the safety-critical task showed a correlation of r = 0.890. These findings suggest that fixation-frequency-based and dwell-time-based entropy measures exhibit substantial overlap across different visual task contexts. However, the observed associations may partly reflect mathematical dependency between fixation frequency and cumulative dwell-time, and the findings should be interpreted as exploratory evidence rather than proof of metric interchangeability. The study highlights that gaze entropy metrics should be interpreted in relation to task-dependent attentional contexts. Higher entropy may be associated with exploratory visual attention in emotional evaluation, whereas lower entropy may be associated with focused monitoring in safety-critical tasks.