minimienergin

Minimienergin, literally "the minimum energy" in Swedish, refers to the broad idea that physical systems tend to adopt configurations that minimize a relevant energy functional under given constraints. It is a central, unifying concept across physics, chemistry, and engineering, expressed in various forms depending on the system and the chosen variables.

In classical and quantum contexts, minimienergin appears as a variational principle. For a system described by coordinates q, the equilibrium state is found by minimizing the total energy E(q) with respect to q, subject to boundary conditions and constraints. In quantum mechanics, the ground-state energy E0 is obtained by the variational principle: for any normalized trial state, the expectation value ⟨ψ|H|ψ⟩ is an upper bound to E0, with equality for the true ground state. Practically, this leads to methods such as the Rayleigh-Ritz procedure and density-functional theory, where the energy functional is minimized with respect to wave functions or electron densities.

In thermodynamics, equilibrium corresponds to extrema of appropriate thermodynamic potentials under given constraints. For isolated systems, the internal energy U is minimized at fixed entropy and volume; at fixed temperature and volume, the Helmholtz free energy F is minimized; at fixed temperature and pressure, the Gibbs free energy G is minimized. These formulations connect microscopic energy to macroscopic observables.

Applications of minimienergin include determining molecular geometries, crystal structures, and reaction pathways, as well as guiding numerical optimization in engineering and materials science. Limitations arise from the presence of local minima, metastable states, and finite-temperature effects, which can obscure the global minimum or require alternative formulations that account for entropy and dynamics.