From free energy measurements to thermodynamic inference in nonequilibrium small systems

Fluctuation theorems (FTs), such as the Crooks or Jarzynski equalities (JEs), have become an important tool in single-molecule biophysics where they allow experimentalists to exploit thermal fluctuations and measure free-energy differences from non-equilibrium pulling experiments. The rich phenomenology of biomolecular systems has stimulated the development of extensions to the standard FTs, to encompass different experimental situations. Here we discuss an extension of the Crooks fluctuation relation that allows the thermodynamic characterization of kinetic molecular states. This extension can be connected to the generalized JE under feedback. Finally we address the recently introduced concept of thermodynamic inference or how FTs can be used to extract the total entropy production distribution in nonequilibrium systems from partial entropy production measurements. We discuss the significance of the concept of effective temperature in this context and show how thermodynamic inference provides a unifying comprehensive picture in several nonequilibrium problems