  The interplay between thermodynamics and information theory has a long
history, but its quantitative manifestations are still being explored. We
import tools from expected utility theory from economics into stochastic
thermodynamics. We prove that, in a process obeying Crooks' fluctuation
relations, every $\alpha$ R\'enyi divergence between the forward process and
its reverse has the operational meaning of the ``certainty equivalent'' of
dissipated work (or, more generally, of entropy production) for a player with
risk aversion $r=\alpha-1$. The two known cases $\alpha=1$ and $\alpha=\infty$
are recovered and receive the new interpretation of being associated to a
risk-neutral and an extreme risk-averse player respectively. Among the new
results, the condition for $\alpha=0$ describes the behavior of a risk-seeking
player willing to bet on the transient violations of the second law. Our
approach further leads to a generalized Jarzynski equality, and generalizes to
a broader class of statistical divergences.
