Expected Behavior of Quantum Thermodynamic Machines with Prior Information

TL;DR

This paper investigates how incomplete information about external parameters influences the expected behavior of quantum heat engines, revealing that prior distributions can lead to thermodynamic-like features in quantum models.

Contribution

It derives a specific prior distribution for unknown parameters and shows how this leads to classical thermodynamic behavior in quantum heat engines.

Findings

Expected values exhibit thermodynamic-like features

Prior distribution is proportional to 1/a_i

Incomplete information can induce classical thermodynamic behavior

Abstract

We estimate the expected behavior of a quantum model of heat engine when we have incomplete information about external macroscopic parameters, like magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters, $a_i, (i=1,2)$. Based on a few simple assumptions, the prior is found to be of the form $\Pi(a_i) \propto 1/a_i$. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamic-like features. This leads us to a surprising proposal that incomplete information quantified as appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.