There is good evidence that a class of conformal gauge theories at strong gauge coupling and for large rank of the gauge group can be described by classical gravity in five dimensions. In this gauge/gravity duality, the theory of classical gravity always admits a consistent truncation to pure gravity so that there is a sector in the dual gauge theories where the dynamics is universal. This universal sector constitutes phenomena like hydrodynamics, but also other phenomena far away from equilibrium such as decoherence and relaxation. We will use field theoretic tools to understand how the time evolution of all states and the expectation values of all observables in the universal sector get determined by the energy-momentum tensor alone. We will find a way to extrapolate our field-theoretic results to strong coupling to propose a condition on the energy-momentum tensor such that the dual solution in gravity has a smooth future horizon, as a test of our approach. We will also do a first study of how irreversibility emerges at long time scales of observation through gravity.