zeroentropy

Zeroentropy is a concept used across physics and information theory to describe a state of complete order or certainty. It is not a single object but appears in several frameworks where the uncertainty about the microstate of a system vanishes or becomes negligible.

In thermodynamics and statistical mechanics, entropy S measures the degree of disorder or the number of accessible microstates. The third law states that the entropy of a perfect crystal at absolute zero is zero. In practice, real materials may exhibit residual entropy due to ground-state degeneracy, so the zero value is an idealization. Zeroentropy implies that, at a given temperature, the microscopic configuration is uniquely determined (or overwhelmingly likely).

In information theory, Shannon entropy H(X) quantifies average uncertainty in a random variable X. H(X) equals zero if X has a single possible outcome with probability one; the symbol carries no information on average, and optimal coding would require no average code length beyond a constant.

In dynamical systems, Kolmogorov-Sinai entropy measures complexity. A system with zero KS entropy has no exponential growth in the number of distinguishable orbits and is considered less chaotic in that sense; such systems can still exhibit rich but predictable long-term behavior.

In quantum information, the von Neumann entropy S(ρ) of a state ρ is zero if and only if ρ is a pure state. Mixed states have positive entropy, reflecting quantum uncertainty about the system.

Zeroentropy is an idealized concept; real systems typically depart from zero due to interactions, finite temperature, or degeneracy. Measurements of entropy depend on the chosen model and level of description.

See also: third law of thermodynamics, residual entropy, Shannon entropy, von Neumann entropy.