  The past twenty years have seen a resurgence of interest in nonequilibrium
thermodynamics, thanks to advances in the theory of stochastic processes and in
their thermodynamic interpretation. Fluctuation theorems provide fundamental
constraints on the dynamics of systems arbitrarily far from thermal
equilibrium. Thermodynamic uncertainty relations bound the dissipative cost of
precision in a wide variety of processes. Concepts of excess work and excess
heat provide the basis for a complete thermodynamics of nonequilibrium steady
states, including generalized Clausius relations and thermodynamic potentials.
But these general results carry their own limitations: fluctuation theorems
involve exponential averages that can depend sensitively on unobservably rare
trajectories; steady-state thermodynamics makes use of a dual dynamics that
lacks any direct physical interpretation. This review aims to present these
central results of contemporary nonequilibrium thermodynamics in such a way
that the power of each claim for making physical predictions can be clearly
assessed, using examples from current topics in soft matter and biophysics.
