Limits to catalysis in quantum thermodynamics

Abstract

Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of thermodynamical processes naturally allows for auxiliary systems dubbed 'catalysts', i.e., any physical systems facilitating state transformations while remaining essentially intact in their state, like an auxiliary system, a clock, or an actual catalyst. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating a state transformation process. To incorporate the genuine physical role of a catalyst, we identify very significant restrictions on arbitrary state transformations under dimension or mean energy bounds, using methods of convex relaxations. We discuss the implication of these findings on possible thermodynamic state transformations in the quantum regime.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 5 Since Gibbs preserving maps in [1] induce the same pre-order structure in the state space as thermal operations for this classical regime (block-diagonal states), our results would apply to the paradigm of Gibbs preserving maps [28] as well.

Toward Physical Realizations of Thermodynamic Resource Theories

“…If TRT predictions are tested in some lab, the catalysts in the lab must be identified. Predictions should be calculated from catalytic thermal operations [28,33]. If predictions are calculated from thermal operations, the neglect of the catalysts must be justified.…”

“…Yet heat, work, and entropy characterize the few-particle scales that experimentalists can increasingly control (e.g., [23][24][25][26][27]), as well as single trials. Small scales have been described by TRTs (e.g., [2,[28][29][30][31][32][33]). These results fall under the umbrella of one-shot statistical mechanics, an application of the one-shot information theory that generalizes Shannon theory [34].…”

“…Precedents for altering the definition of free operations exists: thermal operations are expanded to catalytic thermal operations in [28,33]. Experimentalists use engines, clocks, and other equipment that facilitates transformations without altering (or while altering negligibly).…”

“…A precedent exists for incorporating paid-for measurements into allowed operations: thermal operations have been expanded to catalytic thermal operations [28,33]. Just as catalysts are not free, measurements are not: an agent could pay to restore a degraded catalyst to its initial state and can pay to erase a memory.…”

“…Extracting work at a difficultto-detect cost contradicts the spirit of the First Law of Thermodynamics. Resource theorists have called for eliminating embezzlement from TRTs by redefining thermal operations or by redefining ǫ-approximation [33,49,70]. Three redefinitions have been proposed.…”