Minimum energy of a system

Question

I have always been taught and explained that a system always tries to remain in potential energy configuration. What could be the possible reasons behind it . Is it a universal fact?

Answer 1

The principle of minimum energy is essentially a restatement of the second law of thermodynamics. It states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium. External parameters generally means the volume, but may include other parameters which are specified externally, such as a constant magnetic field.

The term "principle" means that yes, it is considered a universal fact. Principles,laws, postulates are observational/eperimental facts used as axioms in formulating the various physical theories, to pick up from the mathematical solutions those that describe data and predict new situations.

It is one of the basic reasons that quantum mechancal theory developed, because the existence of atoms violates the classical electromagnetic theory: all the electrons should fall on the nucleus and neutralize it for the energy to be minimized. Quantum mechanics by quantising the possible states and defining in the mathematics a ground state saved the minimum energy principle by redefining kinematics in the micrososm of atoms and molecules.

Answer 2

Generally speaking, a potential energy field $U(\mathbf{x})$ defines an associated force $\mathbf{F}(\mathbf{x}) = -\nabla(U)$. This force will be zero when $\nabla(U)$ is zero i.e. when $U(\mathbf{x})$ is a local minimum or maximum. The states $\mathbf{x}$ where $\mathbf{F}(\mathbf{x})$ is zero are said to be in equilibrium.

If $U(\mathbf{x})$ is a local maximum then a small perturbation away from $\mathbf{x}$ will result in a force that is directed away from $\mathbf{x}$ so the perturbation will grow. These states are said to be in unstable equilibrium.

However, if $U(\mathbf{x})$ is a local minimum then a small perturbation away from $\mathbf{x}$ will result in a force that is directed towards $\mathbf{x}$ so the perturbation will not grow. These states are said to be in stable equilibrium.