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In thermal equilibrium each degree of freedom of a physical system (like position x) has an expectation value for its energy of <E>=1/2 kB T, where kB is Boltzmann's constant and T is temperature. If you now measure the energy of the Brownian motion (e.g. <E>=1/2 k <x^2>, if it is a particle connected to a spring k with only degree of freedom x), you can calculate the temperature T=2<E>/k or T=k <x^2>/kB. In other words, the temperature can be determined from the Brownian motion x of the particle if the potential in which the particle is moving is well known. You could call this Brownian motion thermometry.

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Q: What relation does the Brownian movement have to Thermometry?
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