- #1
- 7,861
- 1,598
Those treatments of Entropy in continuum mechanics that I've viewed on the web introduce Entropy abruptly, as if it is a fundamental property of matter. For example the current Wikepedia article on continuum mechanics ( https://en.wikipedia.org/wiki/Continuum_mechanics ) says:
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?
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?