lowestenergy

Lowest energy is a phrase used to describe the state in a physical system with minimum possible energy given the constraints. The lowest-energy state is often called the ground state; many physical processes proceed toward minimizing energy, subject to conservation laws and external conditions.

In quantum mechanics, the energy is quantized and described by the Hamiltonian. The Schrödinger equation yields eigenstates with corresponding eigenvalues; the ground state has the smallest eigenvalue, E0. Systems at long times tend to occupy the ground state if isolated; transitions require energy input.

In classical physics and thermodynamics, a system with potential energy V(r) seeks a configuration that minimizes V. Stable equilibrium occurs at a local minimum of V; at finite temperature, the probability of occupying a higher-energy state is governed by the Boltzmann distribution, so the system samples low-energy configurations with probabilities exp(-ΔE/kT). At zero temperature, the system settles in a minimum-energy configuration.

In chemistry and materials science, molecules adopt lowest-energy conformations to maximize stability. The potential energy surface (PES) maps energy to geometries; search for the global minimum yields the most stable structure; numerical methods such as gradient descent, conjugate gradient, and more advanced optimizers are used to find minima.

In optimization and related fields, minimization of energy is a common metaphor for minimizing an objective function, sometimes called an energy function. Energy minimization underpins simulations in biophysics, condensed matter, and machine learning.