Thermodynamic Efficiency of Self-Organization: Inferential and Information-Geometric Perspectives

The concept of thermodynamic efficiency, drawing from statistical physics and information theory, has previously been proposed to characterize a change in control parameter by relating the resulting predictability gain to the required amount of work. However, previous studies have taken a system-centric perspective and considered only single control parameters. Here, considering systems at or near equilibrium, we generalize thermodynamic efficiency to multiple control parameters and extend the definition of thermodynamic efficiency to protocols in arbitrary directions, by introducing directional efficiency. Taking an observer-centric perspective, we derive two novel formulations. The first, an inferential form, relates efficiency to fluctuations of macroscopic observables, interpreting thermodynamic efficiency in terms of how well the system parameters can be inferred from observable macroscopic behavior. The second, an information-geometric form, expresses efficiency in terms of the Fisher information matrix, interpreting it with respect to how difficult it is to navigate the statistical manifold defined by the control protocol.