The density of seawater controls much of the movement of water, or the thermohaline flow, in the ocean. The density of seawater is primarily determined by the temperature and salinity of that water.  Changes in these two main parameters, potential temperature Θ and salinity S, are multiplied with their thermal expansion  or haline contraction coefficient  equal to each other;  and  are both proportional to a change in density and are both terms of the linearized equation of state of the ocean (TEOS-10). This similarity is supposed to be relevant for understanding the consequences of sea water mixing. 
The density  doesn't change over an isopycnal. However, by mixing a change in temperature and salinity can occur. Therefore spiciness  is introduced as variable that is proportional to thermal expansion and haline contraction. Integration of this variable along an isopycnal leads to the following equation.
Spiciness could be described as the isothermal gradient of the density that equals the isohaline gradient of the density. 
The isopycnal gradient of spiciness should equal to the isopycnal gradient of temperature and salinity by multiplication with the derivative in the other variable of the density.
Another mathematical implication for the existence of a spiciness influence manifests itself in a -diagram, where the negative slope of the isopleths equals the ratio between the temperature- and salinity derivative of the spiciness.