Ignorance based inference of optimality in thermodynamic processes

We derive ignorance based prior distribution to quantify incomplete information and show its use to estimate the optimal work characteristics of a heat engine.

💡 Research Summary

The paper introduces a Bayesian framework for estimating the optimal work output and efficiency of a heat engine when the underlying thermodynamic parameters are unknown. The authors begin by formalizing the notion of “ignorance‑based prior” – a probability distribution that reflects a complete lack of prior information about a parameter such as the intermediate temperature between two reservoirs. To obtain a prior that is invariant under re‑parameterization, they adopt the Jeffreys prior, which is proportional to the square root of the Fisher information. For a temperature variable this leads to (\pi(T)\propto 1/T), embodying scale‑invariance and the idea that no temperature scale is preferred a priori.

The physical model considered is a simple two‑reservoir engine operating between a hot bath at temperature (T_h) and a cold bath at (T_c). Heat is transferred through an intermediate working temperature (T_m) with linear conductances (k_h) and (k_c). The work extracted is (W = k_h (T_h - T_m) - k_c (T_m - T_c)) and the efficiency is (\eta = 1 - \frac{k_c (T_m - T_c)}{k_h (T_h - T_m)}). Because (T_m) is unknown, the authors treat it as a random variable with the Jeffreys prior and compute the Bayesian expectations
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