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The quantity of interest in this case is the entropy. Thus, we assume that there is an entropy flux, an entropy source, and an internal entropy density per unit mass (##\eta##) in the region of interest.

Are other approaches to entropy? Can entropy be defined as a function of the more familiar properties of matter -such as position, mass, velocity?

For example, making an analogy between mass density and a probability density function, one aspect of an alternate definition of entropy ##H_a## could be to define ##H_a## as a function that increases as mass density becomes more uniform. Making an analogy with the entropy of thermodynamics , another aspect could be that at a given constant mass density, ##H_a## is higher when balance of matter at locations ( due to inflow and outflow) takes place at a high rate (- high "turnover"). Is there a specific function of the fundamental properties of matter that meets those requirements and is a useful definition of Entropy?