Informative priors and the analogy between quantum and classical heat engines

Abstract

When incomplete information about the control parameters is quantified as a prior distribution, a subtle connection emerges between quantum heat engines and their classical analogs. We study the quantum model where the uncertain parameters are the intrinsic energy scales and compare with the classical models where the intermediate temperature is the uncertain parameter. The prior distribution quantifying the incomplete information has the form π(x) ∝ 1/x in both the quantum and the classical models. The expected efficiency calculated in near-equilibrium limit approaches the value of one third of Carnot efficiency.

Feynman’s Ratchet and Pawl with Ecological Criterion: Optimal Performance versus Estimation with Prior Information

“…Recently, one of the authors and coworkers [31][32][33][34][35] introduced a novel method of optimization, by which some variables can be assigned values, only in a probabilistic sense. This approach is based on interpreting the limited prior information about the system in the sense of subjective probability [36,37], and a prior distribution quantifies the uncertainty in these parameters.…”

Bounds on thermal efficiency from inference

“…So now we assume to be ignorant about the value T also. To quantify our guess in the absence of the value T , we have to specify a prior distribution for T [13,14], which takes into account our belief as to which value T from the allowed range, the controller may be holding. If we do not have a reason to expect one value over another, then all allowed values are equally likely in the inter-…”

“…This has prompted a fruitful discussion on the role of information theory in thermodynamic frameworks, for example the role of Maxwell's demon in information processing [10] which is continuing to this day. Recently, it has also been explored in [11][12][13][14], that the identification and inclusion of prior information in heat cycles with incomplete specification, leads to interesting analogies with irreversible models. In particular, many different efficiencies show up in the inference based approach which are found in the context of time-dependent cycles or with other sources of irreversibility [15].…”

Quantum Brayton Engine of Non-Interacting Fermions in a One-Dimensional Box

“…The fundamental conceptual difference between these classical and quantum thermal machines is that in the quantum thermal machines one is concerned with the discrete energy levels of particles. In the literature, various examples of quantum thermal machines can be found [30][31][32][33][34][35]. These examples include the quantum analogues of Brayton, Diesel, Lenoir, Carnot, Stirling and Otto cycles [36][37][38][39][40].…”