Computation of the Boltzmann entropy of a landscape: a review and a generalization

Context A key goal of landscape ecology is to understand landscape ecological processes across space and through time, with reference to the central organizing principles of nature. Towards this goal, Boltzmann (or thermodynamic) entropy has been widely used in a conceptual way to link these processes to thermodynamic laws, but it has seldom been computed because of a lack of feasible methods since its formulation in 1872. This situation will probably change because such methods have been developed very recently. Objectives To present a timely, comprehensive review and an analysis of such methods. Methods A systematic survey of the efforts to compute the Boltzmann entropy of a landscape was performed. The consistency of different computational methods was investigated. Results In the review, two classes of methods were identified. The methods were developed from distinct ideas, apply to different landscape models (landscape mosaics and gradients), and result in different Boltzmann entropies. Thus, a general method for both landscape models would be desirable for consistent thermodynamic interpretations. Towards this goal, an approach was suggested to extend the method for mosaics to gradients or vice versa. Possible strategies for both extensions were theoretically analyzed and experimentally tested. Problems of each extension were revealed. Conclusions These recently developed methods can be regarded as first steps in the computation of Boltzmann entropy for landscapes. This computation still requires much attention. Future research is recommended to improve the computation and to apply Boltzmann entropy in the thermodynamic understanding of landscape dynamics.