We introduce a unified framework that relates orbital and heat magnetizations to experimentally accessible excitation spectra, through thermoelectric probes and generalized sum rules. By analyzing zero-temperature transport coefficients and applying Kramers-Kronig relations, we derive spectral representations of magnetization densities from thermoelectric correlation functions. Excitation rates under chiral thermoelectric drives then naturally emerge as direct probes of these Kubo-type correlators, placing orbital and heat magnetizations on equal footing with the topological Chern number. As a direct consequence of our formalism, we introduce a hierarchical construction that organizes orbital and heat magnetizations into distinct physical contributions accessible through sum rules, and also naturally obtain real-space markers of these magnetizations. Besides, nonchiral thermal probes identify a heat quantum metric, which is defined over the space of gravitomagnetic deformations. From an experimental standpoint, we propose concrete implementations of thermoelectric dichroic measurements in quantum-engineered platforms based on modulated strain fields. These results establish thermoelectric dichroic measurements as a versatile route to access and disentangle fundamental ground-state properties.

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• Geometric & topological phases
• Thermal conductivity
• Topological insulators
• Topological materials
• Ultracold gases
• Electron magnetic circular dichroism