Calculating the configurational entropy of a landscape mosaic

Background

Applications of entropy and the second law of thermodynamics in landscape ecology are rare and poorly developed. This is a fundamental limitation given the centrally important role the second law plays in all physical and biological processes. A critical first step to exploring the utility of thermodynamics in landscape ecology is to define the configurational entropy of a landscape mosaic. In this paper I attempt to link landscape ecology to the second law of thermodynamics and the entropy concept by showing how the configurational entropy of a landscape mosaic may be calculated.

Result

I begin by drawing parallels between the configuration of a categorical landscape mosaic and the mixing of ideal gases. I propose that the idea of the thermodynamic microstate can be expressed as unique configurations of a landscape mosaic, and posit that the landscape metric Total Edge length is an effective measure of configuration for purposes of calculating configurational entropy.

Conclusions

I propose that the entropy of a given landscape configuration can be calculated using the Boltzmann equation. Specifically, the configurational entropy can be defined as the logarithm of the number of ways a landscape of a given dimensionality, number of classes and proportionality can be arranged (microstates) that produce the observed amount of total edge (macrostate).