revertibility

Revertibility is the property of a system of processes or mappings whereby the original state can be recovered from the current state, or a reverse operation exists that undoes its effect. In practice, the term is closely related to reversibility, with nuance across disciplines.

In mathematics, a function f: X -> Y is invertible if it is bijective; the inverse function f^-1: Y -> X exists and undoes the effect of f. For linear algebra, a matrix is invertible if its determinant is nonzero, and the inverse matrix satisfies A A^-1 = I. Examples include rotations, which are invertible, while squaring a real number is not invertible without restricting the domain.

In physics, reversible processes can proceed without net entropy production and, in principle, can be reversed to restore the initial state. These processes are idealizations; most real systems exhibit irreversibility due to dissipation and friction. Time-reversal symmetry in the fundamental laws relates to reversibility at the microscopic level, but thermodynamic reversibility is not guaranteed in macroscopic phenomena.

In computing and information, reversible computing aims to perform computations with negligible information loss, reducing energy dissipation in accordance with Landauer’s principle. This involves reversible logic gates, such as the Toffoli gate, which can be run backward. Separately, revertibility also refers to the ability to restore a prior state in software, databases, or version control by undoing changes or performing a revert operation.

Across domains, revertibility underscores a common concept: the existence of an inverse transformation or process that can undo prior effects.