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The minimum total potential energy principle is a fundamental concept used in physics and engineering.It dictates that at low temperatures a structure or body shall deform or displace to a position that (locally) minimizes the total potential energy, with the lost potential energy being converted into kinetic energy (specifically heat).
Energy principles in ... Minimum total potential energy principle; Principle of stationary total complementary potential energy; Castigliano's first theorem ...
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 ...
Therefore, the abbreviated action can be written = = since the kinetic energy = equals the (constant) total energy minus the potential energy (). In particular, if the potential energy is a constant, then Jacobi's principle reduces to minimizing the path length s = ∫ d s {\textstyle s=\int ds} in the space of the generalized coordinates ...
In particular: (see principle of minimum energy for a derivation) [8] When the entropy S and "external parameters" (e.g. volume) of a closed system are held constant, the internal energy U decreases and reaches a minimum value at equilibrium. This follows from the first and second laws of thermodynamics and is called the principle of minimum ...
For many systems, L = T − V, where T and V are the kinetic and potential energy of the system, respectively. [3] The stationary action principle requires that the action functional of the system derived from L must remain at a stationary point (specifically, a maximum, minimum, or saddle point) throughout the time evolution of the system ...
By the principle of minimum energy, there are a number of other state functions which may be defined which have the dimensions of energy and which are minimized according to the second law under certain conditions other than constant entropy. These are called thermodynamic potentials. For each such potential, the relevant fundamental equation ...
The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of N electrons constrained to the surface of a unit sphere that repel each other with a force given by Coulomb's law.