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
Famous quotes containing the words minimum, total, potential, energy and/or principle:
“After decades of unappreciated drudgery, American women just don’t do housework any more—that is, beyond the minimum that is required in order to clear a path from the bedroom to the front door so they can get off to work in the mourning.”
—Barbara Ehrenreich (20th century)
“Of lower states, of acts of routine and sense, we can tell somewhat; but the masterpieces of God, the total growths and universal movements of the soul, he hideth; they are incalculable. I can know that truth is divine and helpful; but how it shall help me I can have no guess, for so to be is the sole inlet of so to know.”
—Ralph Waldo Emerson (1803–1882)
“The real community of man ... is the community of those who seek the truth, of the potential knowers.”
—Allan Bloom (1930–1992)
“In the west, Apollo and Dionysus strive for victory. Apollo makes the boundary lines that are civilization but that lead to convention, constraint, oppression. Dionysus is energy unbound, mad, callous, destructive, wasteful. Apollo is law, history, tradition, the dignity and safety of custom and form. Dionysus is the new, exhilarating but rude, sweeping all away to begin again. Apollo is a tyrant, Dionysus is a vandal.”
—Camille Paglia (b. 1947)
“The principle of asceticism never was, nor ever can be, consistently pursued by any living creature. Let but one tenth part of the inhabitants of the earth pursue it consistently, and in a day’s time they will have turned it into a Hell.”
—Jeremy Bentham (1748–1832)