quasiconserved

The term quasiconserved is used in physics and other scientific fields to describe quantities that are not strictly conserved but change only very slowly or to a very small extent over long periods. This concept arises in systems where exact conservation laws might be violated by small perturbations or approximations.

In Hamiltonian mechanics, a quantity is strictly conserved if its Poisson bracket with the Hamiltonian of the system is zero. If this Poisson bracket is not exactly zero but is very small, the quantity is considered quasiconserved. This often happens when the system is only slightly perturbed from a fully integrable or conserved state. For instance, in celestial mechanics, quantities like energy or angular momentum can be quasiconserved over human timescales, even though gravitational interactions are complex and can lead to slow changes over astronomical epochs.

The notion of quasiconservation is particularly relevant in the study of nearly integrable systems. These are systems that are close to being integrable (meaning they have a sufficient number of conserved quantities for a complete analytical solution). The small deviations from integrability lead to the slow drift of quantities that would be exactly conserved in the perfectly integrable case.

Another context where quasiconservation appears is in statistical mechanics and thermodynamics, especially when dealing with systems that are not in perfect equilibrium. Certain macroscopic properties might appear constant for practical purposes but are slowly evolving due to underlying microscopic interactions. The distinction between conserved and quasiconserved is crucial for understanding the long-term behavior and stability of physical systems, allowing for approximations that simplify analysis without losing essential qualitative features.