Defining the Entropy of Hierarchical Organizations

A measure of the order within a hierarchical organizational structure is proposed based on an analogy with the thermodynamic entropy of physical sciences. Organizational entropy is defined in a manner that readily allows for practical calculations. This calculation could be used to relate the order or entropy of an organization to its functional role. Additionally, it could be used to monitor the change in entropy over time and provide an impetus for periodic restructuring. This theory gives two general contributions to the entropy of an organizational structure: horizontal entropy due to changes within a level of the hierarchy and vertical entropy due to changes between levels along reporting lines within the organization. In addition to employing the thermodynamic entropy analog, identical theoretical results are obtained when calculating the Kolmogorov entropy or algorithmic complexity of an organizational hierarchy and establishes the generality of the approach. Computer simulations on model hierarchical structures show the boundaries of the vertical and horizontal contribution to entropy. It is postulated that each organization will have a specific entropy that optimizes organizational functions.