nonergativity

Nonergativity is a concept arising in statistical mechanics and thermodynamics that describes systems where the properties of a macroscopic sample do not depend on the specific microscopic configurations contributing to the overall macroscopic state. In simpler terms, for a nonergodic system, the time average of a physical quantity will not necessarily equal the ensemble average of that quantity. This is in contrast to ergodic systems, which are assumed to explore all accessible microstates over a sufficiently long time, making time and ensemble averages equivalent.

The assumption of ergodicity is fundamental to many standard thermodynamic derivations, particularly those that rely on the equipartition theorem or the canonical ensemble. When a system is nonergodic, its long-term behavior might be constrained to a subset of its theoretically available states. This can lead to observable differences between the properties measured by observing a single system over a long period and the properties predicted by averaging over a collection of identical, independent systems at a single point in time.

Nonergodicity can manifest in various physical phenomena. For instance, in glasses and spin glasses, the slow relaxation dynamics and the existence of a vast number of metastable states can lead to nonergodic behavior. Similarly, disordered systems and systems exhibiting phase transitions can sometimes display nonergodic characteristics, particularly in the vicinity of the transition. Understanding nonergativity is crucial for accurately describing and predicting the behavior of these complex systems where standard ergodic assumptions break down.