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We review an approach to determine the minimal spatial length scales on which local temperature exists. We first discuss the precise definition of the existence of local temperature and its physical relevance. The approach to calculate the length scales in question considers homogenous chains of particles with nearest-neighbour interactions. The entire chain is assumed to be in a thermal equilibrium state and it is analysed when such an equilibrium state at the same time exists for a local part of it. The result yields estimates for real materials, the liability of which is discussed.

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