E0

E0 is a designation that appears in different disciplines, and its meaning depends on the context. It is not tied to a single universal definition, but rather functions as a label for specific concepts in various fields.

In physics and chemistry, E0 commonly denotes the ground-state energy of a system—the lowest possible energy state. In quantum chemistry and spectroscopy, E0 often refers to the electronic ground-state energy at fixed nuclear geometry, serving as a reference from which excitation energies, zero-point energies, and other thermodynamic quantities are measured. Depending on the calculation, E0 may be reported alongside higher-energy states (e.g., E1, E2) or corrected for zero-point energy.

In descriptive set theory, E0 denotes a standard equivalence relation on the space of infinite sequences, typically on binary or natural-number sequences. Two sequences x and y are considered E0-equivalent if they differ only on finitely many coordinates. E0 is a central object in the study of Borel reducibility and the hierarchy of complexity among equivalence relations, and it serves as a benchmark for comparing complexity across different mathematical structures.

Other uses may occur in specialized domains, but they are usually context-dependent and less standardized. When encountering E0, the intended meaning is typically clarified by the subject area, accompanying notation, or the described problem.