Gleichgewichtsproblemen

Gleichgewicht, from the German root for balance, denotes a state in which a system's opposing influences balance out, producing stability over time. It encompasses static and dynamic forms. In static equilibrium, the net external forces and torques vanish, so objects remain at rest or in a constant motion with zero acceleration. In dynamic equilibrium, processes continue but macroscopic properties stay constant because rates of opposing processes are equal.

Chemical equilibrium occurs in reversible reactions when the forward and reverse reaction rates are equal, yielding constant concentrations. The position shifts with changes in concentration, temperature, or pressure, as described by Le Chatelier's principle and quantified by an equilibrium constant K.

Thermodynamic equilibrium describes no net exchange of energy or matter with surroundings; temperature, pressure, and chemical potentials are uniform throughout the system, and no driving forces remain. In mechanics, static equilibrium is a special case where even torques cancel.

In economics, market equilibrium arises when supply matches demand at a certain price, prompting no inherent pressure for price change absent external shifts.

In biology and ecology, homeostasis and ecosystem stability refer to biological and environmental equilibria, though natural systems can show fluctuations or cyclical dynamics rather than a fixed balance.

Mathematically, equilibria are steady-state solutions where derivatives vanish; analyzing their stability helps predict responses to perturbations.