On Incompatible Descriptions of Systems Across Scales of Granularity

Abstract

The scientific description of any system depends on the target properties of that description. A detailed, fine-grained account of all individual constituents of a system differs from that of properties at larger scales of granularity, up to the system as a whole. All these level-specific descriptions can be compatible or incompatible with one another. This contribution addresses a particular pair of descriptions of complex dynamical systems: their Liouville dynamics, treating each constituent separately in a conventional state space, and their information dynamics, based on partitions of that state space. The relation between them can be formulated as a commutation relation, in which the commutator quantifies the degree of their incompatibility.