For a single enzyme or molecular motor operating in an aqueous solution of
non-equilibrated solute concentrations, a thermodynamic description is
developed on the level of an individual trajectory of transitions between
states. The concept of internal energy, intrinsic entropy and free energy for
states follows from a microscopic description using one assumption on
time-scale separation. A first law energy balance then allows the unique
identification of the heat dissipated in one transition. Consistency with the
second law on the ensemble level enforces both stochastic entropy as third
contribution to the entropy change involved in one transition and the local
detailed balance condition for the ratio between forward and backward rates for
any transition. These results follow without assuming weak coupling between the
enzyme and the solutes, ideal solution behavior or mass action law kinetics.
The present approach highlights both the crucial role of the intrinsic entropy
of each state and the physically questionable role of chemiostats for deriving
the first law for molecular motors subject to an external force under realistic
conditions.Comment: 11 page
