Maxwell... during the 1860s... showed that when the velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwell's results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities. (James Clerk Maxwell)

Maxwell... during the 1860s... showed that when the velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwell's results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities.

James Clerk Maxwell

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change distribution equilibrium game likely molecular molecule nash net set slow specific speed state maxwell

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