THERMODYNAMICS OF QUANTUM CONTROL: WORK, HEAT, AND OPTIMALITY IN THE PRESENCE OF COHERENCE
Quantum thermodynamics extends thermodynamic laws to the microscopic regime, where
phenomena such as quantum fluctuations, correlations, and coherence fundamentally alter
energy exchanges. Within this context, this thesis investigates the interplay between
nonequilibrium thermodynamics and informational resources, combining theoretical devel-
opments with numerical simulations and experimental implementations in Liquid-State
Nuclear Magnetic Resonance (NMR). We begin by addressing the foundations of quantum
work and fluctuation relations, employing the framework of Quantum Bayesian Networks
(QBNs) to consistently capture coherent quantum effects. Turning to nonequilibrium
dynamics, we present the experimental observation of the genuine Quantum Mpemba
Effect. By tomographically characterizing the implemented thermalization process and
verifying its Davies-type structure, we experimentally confirm that the suppression of
quantum coherence, coupled with the map’s spectral properties, drives the anomalous
relaxation and free-energy crossings characteristic of this effect. We then actively harness
this phenomenon to enhance the performance of a quantum Otto refrigerator. Next, we
characterize the thermodynamic optimality of quantum coherence. By deriving marginal
fluctuation theorems that account for coherence and athermality, we experimentally im-
plement an optimal quantum work extraction protocol, demonstrating that coherence
serves as an operational resource capable of enhancing work extraction beyond classical
limits. Finally, we address the dissipative counterpart of these processes by formulating
heat exchange in Liouville space. We derive rigorous bounds on heat dissipation and
show that partial thermalization dynamics can induce transient violations of standard
asymptotic limits. Collectively, these results contribute to a broader understanding of how
quantum informational properties act as active operational resources, providing concrete
experimental and theoretical support for their role in nonequilibrium thermodynamic
protocols.