Two approaches to small-scale and quantum thermodynamics are fluctuation relations and oneshot statistical mechanics. Fluctuation relations (such as Crooks' theorem and Jarzynskiʼs equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches feature the same notions of work and the same notions of probability distributions over possible work values. The two approaches are alternative toolkits with which to analyze these distributions. To combine the toolkits, we show how one-shot work quantities can be defined and bounded in contexts governed by Crooks' theorem. These bounds provide a new bridge from one-shot theory to experiments originally designed for testing fluctuation theorems.

Causal asymmetry is one of the great surprises in predictive modelling: the memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modelling a stochastic process where memory costs are minimal. Models operating in the other direction incur an unavoidable memory overhead. Here we show that this overhead can vanish when quantum models are allowed. Quantum models forced to run in the less natural temporal direction not only surpass their optimal classical counterparts, but also any classical model running in reverse time. This holds even when the memory overhead is unbounded, resulting in quantum models with unbounded memory advantage.