Generalising thermodynamic efficiency of interactions: inferential, information-geometric and computational perspectives

Abstract Self-organizing systems consume energy to generate internal order. The concept of thermodynamic efficiency, drawing from statistical physics and information theory, has previously been proposed to characterise 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 generalise 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 behaviour. 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. This observer-centric perspective is contrasted with the existing system-centric view, where efficiency is considered an intrinsic property of the system.