# A = TΔS – ΔH

In equations, the function: $A = T \Delta S - \Delta H \,$

is called “[name]” and is the relation between chemical affinity A of reactants in an isothermal isobaric system and the bound energy TΔS and enthalpic energy ΔH of the system. With substitution of the enthalpy function: $H = U + PV \,$

into the affinity equation, we have: $A = T \Delta S - \Delta U - P \Delta V \,$

which means that affinity (bonding/reaction force), specifically affinity between reactants (or people), i.e. the force of reaction between people, is a function of temperature, entropy, internal energy, pressure, and volume. This means that affinity will be favored, between two people, when there is an increase in entropy, a decrease in internal energy, and a decrease of volume, of the interactive system, over time. One can expand on this equation in more detail, by noting that German physicist Rudolf Clausius defined internal energy of the system, which in this case concerns a system of interacting people or human molecules, as the sum of the vis viva Tv and the ergal Je or $U = T_v + J_e \,$

which when referring to a change Δ over time is: $\Delta U = \Delta T_v + \Delta J_e \,$

Subsequently, the measure of the affinity between two people, wherein A > 0 for spontaneously favored relationships (or ΔG < 0, thermodynamic sense, i.e. according to the spontaneity criterion), is expressed by the equation: $A = T \Delta S - P \Delta V - \Delta T_v - \Delta J_e \,$

meaning that in addition to an entropy increase, ΔS > 0, or transformational content increase (meaning that heat was transformed into system internal evolution work), which signifies that the body or boundaried system of the relationship has transformed or evolved over time, and a volume decrease, ΔV < 0, associated with favorable relationships, meaning that spatial movements of the pair come together over time rather than diverging (simplified by saying that two homes become one), a vis viva decrease, ΔT < 0, and an ergal decrease, ΔJ < 0, will also be associated with favored relationships.

A decrease in vis viva seems to make intuitive sense, in that a couple nearing their golden wedding anniversary will invariably tend to have less kinetic energy then a newly minted couple, in the sense that the former's daily movements will often be slow and tending to be confined to the kitchen, bathroom, and television room. The subject of an ergal decrease over time as associated with stable relationships requires more thought. In formulaic terms, ergal change over time is defined as: $\Delta J_e = J_{e_f} - J_{e_i} \,$

Thus, a negative ergal change, which be the above reasoning is associated with favored relationships, implies that the ergal at the start of the relationship, Ji, must be greater than the ergal at the end of the relationship, Jf.

In the terminology of William Hamilton, an "ergal decrease" is expressed by saying that their was a decrease in the force function of the relationship (system) over time; or in the terminology of William Rankine, this is expressed by saying that there was a decrease in the potential energy of the relationship (system) over time.