Minimum Total Potential Energy Principle
The principle of minimum total potential energy is a fundamental concept used in physics, chemistry, biology, and engineering. It asserts that a structure or body shall deform or displace to a position that minimizes the total potential energy, with the lost potential energy being dissipated as heat. For example, a marble placed in a bowl will move to the bottom and rest there, and similarly, a tree branch laden with snow will bend to a lower position. The lower position is the position for minimum potential energy: it is the stable configuration for equilibrium. The principle has many applications in structural analysis and solid mechanics.
The tendency to minimum total potential energy is due to the second law of thermodynamics, which states that the entropy of a system will maximize at equilibrium. Given two possibilities - a low heat content and a high potential energy, or a high heat content and low potential energy, the latter will be the state with the highest entropy, and will therefore be the state towards which the system moves.
The principle of minimum total potential energy should not be confused with the related principle of minimum energy which states that for a system that changes without heat transfer, the total energy will be minimized.
Note that in most complex systems there is one global minimum and many local minima (smaller dips) in the potential energy. These are called metastable states. A system may reside in a local minimum for a long time — even an effectively infinite period of time.
Read more about Minimum Total Potential Energy Principle: Some Examples, Structural Mechanics
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