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Chemophoresis describes the displacement of a particle in an ambient fluid due to a gradient in chemical composition. Classic phoresis can be understood through linear-response theory: in the presence of a sufficiently small, externally imposed gradient $(\nabla n)_\mathrm{ext}$ in concentration, the phoretic velocity of the particle is $\mathbf{V} = \mathcal{L}_\mathrm{lin}(\nabla n)_\mathrm{ext}$, in terms of the phoretic coefficient $\mathcal{L}_\mathrm{lin}$ given by a Green-Kubo expression.
Self-phoretic particles induce a composition gradient $(\nabla n)_\mathrm{act}$ through catalytic activity and provide a physical realization of artificial swimmers. Experimental observations are then customarily addressed as another instance of classic phoresis, $\mathbf{V} = \mathcal{L}_\mathrm{lin}(\nabla n)_\mathrm{act}$.
However, an additional role of the particle's chemical activity has been recently identified as responsible for a specific activity-induced response $\mathcal{L}_\mathrm{act}$, so that one has to write $\mathbf{V} = \left( \mathcal{L}_\mathrm{lin} + \mathcal{L}_\mathrm{act}\right) \left[ (\nabla n)_\mathrm{ext} + (\nabla n)_\mathrm{act} \right]$ in the more general scenario. This means a change in paradigm as it disproves the claim that ``self-phoresis is phoresis in a self-induced gradient''.
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