Entropy signatures of interstate aggression on social cohesion dynamics

Abstract

This study proposes a systems approach to explore the entropy signatures of war phases on social cohesion dynamics in Ukraine (2004-2025). Using a psycholinguistic time series of online searches for first-person plural pronouns, we quantified social cohesion complexity using sample entropy and refined composite multiscale entropy (RCMSE). Analyses reveal distinct signatures between war phases over time for both metrics, with, respectively, R ² = 0.57 and R ² = 0.95. Relative to peace and full invasion, social cohesion entropy decreased under partial invasion and displayed more anti-persistent behaviour. While social cohesion was most dysfunctional under partial invasion, entropy signatures of full-scale invasion and peace were relatively close. These results offer insights into the impact of interstate aggression on social cohesion and contribute to a dynamical systems understanding of warfare as a systemic shock. The methodology provides a framework for monitoring and predicting societal resilience in response to significant events.

Keywords: Ukraine; aggression; dynamical systems; entropy; social cohesion; themodynamics; warfare.

Figure 1.

Psycholinguistic indicators of social cohesion in Ukraine. Top: weekly Google Trends frequencies for first-person plural pronouns. Bottom: cohesion index $C(t)$ derived from the normalized average of the six pronoun series.

Figure 2.

Cohesion index across phases. Left: a half-eye density plot with boxplots. Right: a beeswarm plot with individual observations, mean values and bootstrapped confidence intervals.

Figure 3.

Entropy levels decrease and decay faster during the partial invasion phase (orange) relative to full invasion (red) and peacetime (green). (A) Weekly sample entropy levels from 2004 to 2025. (B) RCMSE across war phases and over time scales $\tau =15$. (C) Interaction plot from the quadratic mixed-effects model of sample entropy dynamics across phases and over standardized phase duration. (D) Log–log plot of the interaction from the general linear model of RCMSE dynamics across phases and over time scales $\tau =15$. Lines represent polynomial (A–C; 2nd order) and linear (D) fits.