Given the growing prevalence of authoritarian regimes and the emergence of anti-liberal tendencies in certain established democracies, gaining insight into the dynamic and statistical characteristics of political regimes is crucial. Despite their relevance, a comprehensive quantitative assessment of these dynamics on a historical scale remains largely unexplored. I will present a rigorous and quantitative analysis of the dynamic and statistical properties of political regimes worldwide by examining changes in freedoms of expression, association, and electoral quality throughout the 20th century. To do so, we used the multidimensional and disaggregated V-Dem dataset, which covers over 170 countries across more than a century, and we analyzed it with tools from statistical physics. We explored these dynamics using the Diffusion Map dimensionality-reduction technique applied to V-Dem data (1900-2021). Our analysis reveals that changes in freedoms of expression, association, and electoral quality follow a power-law distribution, indicating that political regimes exhibit scale-free dynamics. Through the lens of anomalous diffusion, we identified three distinct classes of dynamics in the data which are clearly dependent on the regime type. I will also present some work in progress. A stability analysis of the country dynamics reveals a sharp decline in stability around the year 2010. I will discuss potential explanations for this observation. This work presents a novel approach to the study of political systems. Our quantitative methodology promotes a bridge between political science and the physics of complex systems.