Symmetry-induced maximum entropy production in enzyme kinetics: A noether-type mechanism

We investigate the maximum entropy production principle (MEPP) in a minimal two-state enzymatic cycle at a nonequilibrium steady state. Using master-equation kinetics, we show that maximal entropy production arises not by explicit extremization but from internal kinetic constraints together with statistically symmetric occupancy of enzyme states. Under these conditions, the Briggs–Haldane steady-state flux equals the structural upper limit set by the catalytic scheme, while the total thermodynamic force is a constant determined solely by intrinsic unimolecular rates. At the microscopic level, a uniform distribution over configurations admits a Lie group of infinitesimal rotations that leave the probability distribution, flux, and force invariant; hence the entropy-production functional is invariant. This yields a Noether-type interpretation of MEPP: maximal entropy production is a structural invariant of an internally organized enzymatic cycle, rather than an externally imposed variational optimum.