Thermal Processes and State Achievability

TL;DR

This paper provides a comprehensive geometric characterization of states achievable through Thermal Processes, revealing the structure of extremal transformations and their graph-theoretic properties in quantum thermodynamics.

Contribution

It introduces a complete thermomajorization-based geometric framework and identifies extremal thermal processes, including non-implementable extremals, for dimensions four and higher.

Findings

Vertices, edges, and facets of achievable states are characterized via thermomajorization curves.

Extremal thermal processes are linked to transportation matrices and include non-implementable extremals.

Biplanarity distinguishes necessary extremal processes from non-essential ones.

Abstract

A complete characterization of the set of states that can be achieved through Thermal Processes (TP) is given by describing all vertices, edges and facets of the allowed set of states in the language of thermomajorization curves. TPs are linked to transportation matrices, which leads to the existance of extremal TPs that are not required in implemenation of any transition allowed by TPs, for every dimension $d\geq 4$ of the state space. A property of the associated graphs, biplanarity, which differentiates between these extremal TPs and the necessary ones, is identified.