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We discuss the emergence of time in quantum gravity, and ask whether time isalways "something that flows"'. We first recall that this is indeed the case inboth relativity and quantum mechanics, although in very different manners: timeflows geometrically in relativity (i.e. as a flow of proper time in the fourdimensional space-time), time flows abstractly in quantum mechanics (i.e. as aflow in the space of observables of the system). We then ask the same questionin quantum gravity, in the light of the thermal time hypothesis of Connes andRovelli. The latter proposes to answer the question of time in quantum gravity(or at least one of its many aspects), by postulating that time is a statedependent notion. This means that one is able to make a notion oftime-as-an-abstract-flow - that we call the thermal time - emerge from theknowledge of both: 1) the algebra of observables of the physical system underinvestigation, 2) a state of thermal equilibrium of this system. Formally, thisthermal time is similar to the abstract flow of time in quantum mechanics, butwe show in various examples that it may have a concrete implementation eitheras a geometrical flow, or as a geometrical flow combined with a non-geometricaction. This indicates that in quantum gravity, time may well still be"something that flows" at some abstract algebraic level, but this does notnecessarily imply that time is always and only "something that flows" at thegeometric level.

Emergence of time in quantum gravity: is time necessarily flowing ?