<p>The existing thermal analysis techniques to study reactions were based on the overall information from detection signals. The overall information represents the integrated behavior of all substances and reactions in terms of quantity and species. As a scalar, it cannot mathematically and physically resolve the high-dimensional information of reactions. In this paper, a linear spatial system for substances and reactions is constructed, based on absolute quantity mole, to achieve dual identification of substances and reactions, analyze the coupling relationships among complex multiple reactions, and utilize vectorization methods to clarify the nonlinear mapping relationship between substance space and reaction space. Thus, the theory and implementation of vector thermal analysis (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\upnu }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">ν</mi> </math></EquationSource> </InlineEquation> TA) exactly align with the physical essence of reactions. Through experimental examples of typical gas–solid phase reactions and coexistence of multiple reactions, the accuracy and reliability of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\upnu }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">ν</mi> </math></EquationSource> </InlineEquation> TA from substance to reaction are verified.</p> Graphical Abstract <p></p>