Bounds on Thermal Efficiency from Inference

TL;DR

This paper uses inference to analyze how uncertainty in thermodynamic parameters affects the maximum achievable efficiency of work extraction from heat reservoirs, revealing bounds below the Carnot limit.

Contribution

It introduces an inference-based approach to quantify how incomplete information reduces the maximum thermal efficiency in thermodynamic processes.

Findings

Efficiency drops to Curzon-Ahlborn value under maximum uncertainty.

Near-equilibrium efficiency scales as half of Carnot efficiency with full information.

Average efficiency estimate decreases to one-third of Carnot efficiency with uncertain labels.

Abstract

The problem of inference is applied to the process of work extraction from two constant heat capacity reservoirs, when the thermodynamic coordinates of the process are not fully specified. The information that is lacking, includes both the specific value of a temperature as well as the label of the reservoir to which it is assigned. The estimates for thermal efficiency reveal that uncertainty regarding the exact labels, reduces the maximal efficiency below the Carnot value, its minimum value being the well known Curzon-Ahlborn value. We also make an average estimate of the efficiency {\it before} the value of the temperature is revealed. It is found that if the labels are known with certainty, then in the near-equilibrium limit the efficiency scales as 1/2 of Carnot value, while if there is maximal uncertainty in the labels, then the average estimate for efficiency drops to 1/3 of Carnot value. We also suggest how infered properties of the incomplete model can be mapped to a model with complete information but with an additional source of thermodynamic irreversibility.