  A non-equilibrium steady state is characterized by a non-zero steady
dissipation rate. Chemical reaction systems under suitable conditions may
generate such states. We propose here a method that is able to distinguish
states with identical values of the steady dissipation rate. This necessitates
a study of the variation of the entropy production rate with the experimentally
observable reaction rate in regions close to the steady states. As an
exactly-solvable test case, we choose the problem of enzyme catalysis. Link of
the total entropy production with the enzyme efficiency is also established,
offering a desirable connection with the inherent irreversibility of the
process. The chief outcomes are finally noted in a more general reaction
network with numerical demonstrations.
