Complementary aspects of non-equilibrium thermodynamics

Bio-molecules are active agents in that they consume energy to perform tasks. The standard theoretical description, however, considers only a system-external work agent. Fluctuation theorems, for example, do not allow work-exchange between fluctuating molecules. This tradition leaves `action through work', an essential characteristic of an active agent, out of proper thermodynamic consideration. Here, we investigate thermodynamics that considers internal-work. We find a complementary set of relations that capture the production of free energy in molecular interactions while obeying the second law of thermodynamics. This thermodynamic description is in stark contrast to the traditional one. A choice of an axiom whether one treats a portion of Hamiltonian as `internal-work' or `internal-energy' decides which of the two complementary descriptions manifests among the dual. We illustrate, by examining an allosteric transition and a single-molecule fluorescence-resonance-energy-transfer measurement of proteins, that the complementary set is useful in identifying work content by experimental and numerical observation.