Mutual constraint as internal energy (more thoroughly explained)

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2024-07-30 17:00:03

This is expanding on the essay written here, illustrating how mutual constraint on probability distributions increases the internal energy of a system. With the implication that a group of people or other entities which have mutually constrained each other’s behavior have increased their internal energy.

If a box of particles has a certain probability distribution, and that probability distribution has a certain equilibrium, or most probable state, then any constraint to that probability distribution can be seen as increasing energy, or storing potential energy. You could also say that this is a reduction of entropy compared to the original distribution.

This is because increasing the probability of one part of the distribution must be done at the expense of other parts of the distribution (because in the end it must add up to 1). If we increase the probability of one state and decrease the probability of another state in a reversible way, we know that when we reverse it (i.e. “release the constraint”) that there will be a greater number of transitions from the states with increased probability to the states with decreased probability when the probability distribution returns to normal. The asymmetry of transitions can then be harnessed and converted to energy of another form because a mechanism can be set up which anticipates this flow. This is a restatement of the second law of thermodynamics which states that an increase in entropy corresponds to an increase of available energy per unit temperature.

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