# Σ(ΔG < 0) + Σ(ΔG > 0) < 0

In equations, the following expression:

is called the Lipmann coupling inequality and quantifies free energy coupling for natural earth-bound processes and reactions occurring at or near the surface of the earth, where the quantity to the left of the inequality:

$\Delta G_T = \sum_{k=i}^j \Delta G_N + \sum_{i=1}^k \Delta G_{\tilde N} \,$

is defined as the "total" system Gibbs free energy change $\Delta G_T \,$, where $\Delta G_{N_i} \,$ refers to an individual, naturally occurring, system constrained process or reaction, defined by the Lewis inequality for a natural processes (ΔG < 0), where $\Delta G_{\tilde N_i} \,$refers to an individual, unnaturally occurring, system constrained process or reaction, defined by the Lewis inequality for an unnatural processes (ΔG > 0), where the summation:

$\sum_{k=i}^j \Delta G_N \,$

is the sum of the Gibbs free energy changes for all "natural", symbol $N \,$, processes or reactions in a given coupled system, where the summation:

$\sum_{i=1}^k \Delta G_{\tilde N} \,$

is the sum of the Gibbs free energy changes for all "unnatural", symbol $\tilde N \,$, processes or reactions in a given coupled system.

Morality
The Lipmann coupling inequality succinctly captures the age old idiom or belief that good always triumphs over evil or in thermodynamic terms natural processes always triumphs over unnatural processes. [1]

Etymology
The above equation is an EoHT assigned name, named after German-born American Fritz Lipmann who in 1941 “Metabolic Generation and Utilization of Phosphate Bond Energy” did the first work in the development of free energy coupling theory, specifically applied to frog leg contraction energy puzzle.

References
1. Thims, Libb. (2011). Thermodynamic Proof that Good Always Triumphs over Evil”, Journal of Human Thermodynamics, 7: 1-4.