Informational non-equilibrium concentration

TL;DR

This paper investigates the possibility of increasing local informational non-equilibrium in quantum systems through unitary evolution, revealing limitations in two-qubit systems and solutions in higher dimensions, with implications for quantum thermodynamics.

Contribution

It analytically solves the problem of concentrating informational non-equilibrium, showing impossibility in two-qubits and feasibility in higher dimensions, and uncovers a Mepmba-like effect in two-qutrits.

Findings

Impossible to concentrate in two-qubits

Achievable in higher-dimensional systems

Discovery of a Mepmba-like effect in two-qutrits

Abstract

Informational contributions to thermodynamics can be studied in isolation by considering systems with fully-degenerate Hamiltonians. In this regime, being in non-equilibrium -- termed informational non-equilibrium -- provides thermodynamic resources, such as extractable work, solely from the information content. The usefulness of informational non-equilibrium creates an incentive to obtain more of it, motivating the question of how to concentrate it: can we increase the local informational non-equilibrium of a product state $\rho\otimes\rho$ under a global closed system (unitary) evolution? We fully solve this problem analytically, showing that it is impossible for two-qubits, and it is always possible to find states achieving this in higher dimensions. Specifically for two-qutrits, we find that there is a single unitary achieving optimal concentration for every state, for which we uncover a Mepmba-like effect. We further discuss the notion of bound resources in this framework, initial global correlations' ability to activate concentration, and applications to concentrating purity and intrinsic randomness.