Understanding how information is dynamically accumulated and transformed in human reasoning has long challenged cognitive psychology, philosophy, and artificial intelligence. Existing accounts, from classical logic to probabilistic models, illuminate aspects of output or individual modelling, but do not offer a unified, quantitative description of general human reasoning dynamics. To solve this, we introduce Information Flow Tracking (IF-Track), that uses large language models (LLMs) as probabilistic encoder to quantify information entropy and gain at each reasoning step. Through fine-grained analyses across diverse tasks, our method is the first successfully models the universal landscape of human reasoning behaviors within a single metric space. We show that IF-Track captures essential reasoning features, identifies systematic error patterns, and characterizes individual differences. Applied to discussion of advanced psychological theory, we first reconcile single- versus dual-process theories in IF-Track and discover the alignment of artificial and human cognition and how LLMs reshaping human reasoning process. This approach establishes a quantitative bridge between theory and measurement, offering mechanistic insights into the architecture of reasoning.