A Demon that remembers: An agential approach towards quantum thermodynamics of temporal correlations

TL;DR

This thesis introduces a decision-theoretic framework for quantum thermodynamics, demonstrating how adaptive strategies and reinforcement learning can enhance work extraction from quantum temporal correlations.

Contribution

It develops the TOFE bound, formalizes adaptive thermodynamic gaps, and applies reinforcement learning to optimize work extraction from unknown quantum sources.

Findings

Adaptive strategies surpass non-adaptive bounds in work extraction.

TOFE provides a new upper bound linked to adaptive ordered discord.

Reinforcement learning achieves polylogarithmic dissipation in quantum state learning.

Abstract

This thesis develops a decision-theoretic framework for extracting thermodynamic work from temporal correlations in quantum systems. We model a classical agent -- lacking quantum memory -- performing adaptive work extraction through continuous inference and decision-making under uncertainty. By introducing $\rho^*$-ideal protocols, we demonstrate that exploiting memory effects allows adaptive strategies to surpass non-adaptive bounds. We formalize this via the Time-Ordered Free Energy (TOFE), a novel upper bound for causal, adaptive operations that reveals a thermodynamic gap linked to adaptive ordered discord. Additionally, we tackle work extraction from unknown sources using reinforcement learning. By adapting multi-armed bandit algorithms, we show an agent can simultaneously learn an unknown i.i.d. quantum state and extract work, achieving polylogarithmic cumulative dissipation that significantly outperforms standard tomography. Overall, this work lays the foundation for predictive and learning-based quantum thermodynamics.