Financial Entropy as a Measure of Disorder And Opacity in the Anti–Money Laundering Context A Mathematical–Physical Approach and Empirical Analysis For The New Era Of Digital Finance

This research proposes the innovative application of principles from Thermodynamics and Statistical Mechanics—particularly the concept of entropy—to quantify the intrinsic disorder and opacity of money-laundering operations. Traditionally, AML efforts have relied on predefined rules and indicators, often insufficient to counter increasingly sophisticated and adaptive schemes in the era of digital finance. This study introduces “financial entropy” as an innovative metric to analyse and detect anomalies in transactional flows. Starting from the physical definition of entropy as a measure of disorder or uncertainty in a system, the research explores how launderers deliberately increase such entropy through transaction multiplication, counterparty diversification, pathway complexity, and commingling, thereby obscuring both the origin and destination of funds. The paper develops a rigorous methodological framework for computing different forms of entropy (Shannon, Rényi, Tsallis) applied to multiple transaction-data attributes such as amounts, frequencies, counterparties, timing, geolocations, and asset types. This analysis is integrated with Network Theory, modelling transactions as flows through a financial network where entropy characterises the “turbulence” or “diffusion” of illicit funds, and with concepts from Chaos Theory and Fractal Geometry to capture the structured complexity of layering. The objective is to provide financial institutions and Financial Intelligence Units (FIUs) with robust analytical tools. The research aims to empirically demonstrate—using aggregated data and real-world laundering typologies (from international bodies such as the FATF and from cybercrime analyses)— how financial entropy may enhance the predictive capability of AML systems and contribute to a reduction in false positives (which generate substantial operational costs) and identify emerging laundering schemes. This approach provides a stronger, scientifically grounded basis for detecting and reporting suspicious transactions (SARs).