Incomplete Information and Expected Performance Characteristics of Heat Engines

Abstract

In this paper, a connection between Bayesian statistics and the optimal performance characteristics of thermodynamic heat cycles is proposed. In particular, the subjective ignorance about internal energy scales of the working medium, quantified as a prior distribution leads to an expected behaviour of heat cycles which shows some remarkable thermodynamic features. It is shown that efficiency at maximum work is closely related to Curzon-Ahlborn (CA) efficiency. This efficiency usually appears in finite-time models of idealised heat engines, where it is associated with efficiency at maximum power. The question of assigning a unique prior for this problem is addressed and it is shown that for a class of priors, the efficiency at optimal performance shows a universal behaviour. Bayes’ theorem is invoked to show how measurements performed on the working medium at various stages of the cycle, lead to this universal behaviour. The proposed connection will be highlighted for both quantum and classical models.

Keywords: Bayesian statistics, thermodynamics, efficiency