referees for useful comments and suggestions and to Andreas Nold for stimulating discussions that led to the scaling arguments in Appendix B. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from EPSRC via grants No. EP/L020564 and EP/L025159.

Derivation of generalised Langevin equations {#app:projection-operator-tech}
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The Fokker-Planck Equation
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Here we outline the derivation of the time-evolution equation for the probability distribution function of a system of arbitrary-shape particles. This derivation can be thought as an application of the works of @kirkwood_statistical_1946, @murphy_brownian_1972, @deutch_molecular_1971 and @wilemski_derivation_1976 in conjunction with the results of @dahler_kinetic_1963, @condiff_brownian_1966, @evans_cumulant_1976 and @condiff_transport_1969, to consider arbitrary-shape particles. .

As in Section \[sec:evolution-equations\], consider $N$ identical, asymmetric colloidal particles with mass $m$ immersed in a fluid of $n\gg N$ identical bath particles with mass $m_b$. Throughout this section upper case letters will refer to colloidal particles while lower case ones indicate bath particles. The phase-space coordinates of the $i$-th bath particle are $\mathbf{x}_j\doteq(\mathbf{r}_j,\,\mathbf{p}_j)$, with “$\doteq$” denoting “by definition", $\mathbf{r}_j$ being the position vector and $\mathbf{p}_j=m_b\dot{\mathbf{r}}_j$ the canonical momentum. In addition, the dynamical state of the $j$-th colloidal particle is determined by $\mathbf{X}_j\doteq(\mathbf{R}_j,\mathbf{P}_j)$, where $\mathbf{R}_j$ is its centre-mass position vector and 