Decomposability and Convex Structure of Thermal Processes

TL;DR

This paper investigates the structure and decomposability of thermal processes in quantum systems, revealing temperature-dependent properties and limitations on work extraction, with detailed analysis for three-level systems.

Contribution

It characterizes extremal thermal processes, their decomposability, and links these to thermomajorization and detailed balance, advancing understanding of quantum thermodynamic transformations.

Findings

Identified extremal points of thermal operations for three-level systems

Connected thermal process structure with thermomajorization criteria

Showed temperature influences the decomposability and work extraction limits

Abstract

We present an example of a Thermal Process for a system of $d$ energy levels, which cannot be performed without an instant access to the whole energy space. This Thermal Process is uniquely connected with a transition between some states of the system, that cannot be performed without access to the whole energy space even when approximate transitions are allowed. Pursuing the question about the decomposability of Thermal Processes into convex combinations of compositions of processes acting non-trivially on smaller subspaces, we investigate transitions within the subspace of states diagonal in the energy basis. For three level systems, we determine the set of extremal points of these operations, as well as the minimal set of operations needed to perform an arbitrary Thermal Process, and connect the set of Thermal Processes with thermomajorization criterion. We show that the structure of the set depends on temperature, which is associated with the fact that Thermal Processes cannot increase deterministically extractable work from a state -- the conclusion that holds for arbitrary $d$ level system. We also connect the decomposability problem with detailed balance symmetry of an extremal Thermal Processes.