The entanglement and coherence of the wobbling mode are studied in the framework of the particle plus triaxial-rotor model for the one-quasiparticle nucleus
135Pr and the two-quasiparticles nucleus
130Ba. The focus lies on the coupling between the total and the particle angular momenta. Using the Schmidt decomposing, it is quantified in terms of the von Neumann entropy of the respective subsystems, which measures their mutual entanglement. The entropy and the entanglement increase with spin
I and number of wobbling quanta
n. The coherence of the wobbling mode is studied by means of the eigenstate decomposition of its reduced density matrix. To a good approximation, the probability distributions of the total angular momentum can be interpreted as the incoherent combination of the coherent contributions from the first two pairs of eigenvectors with the largest weight of the reduced density matrix. Decoherence measures are defined, which, in accordance, scatter between 0.1 to 0.2 at low spin and between 0.1 and 0.3 at high spin. Entanglement in the framework of the adiabatic approximation is further analyzed. In general, the coherent eigenstates of the effective collective Hamiltonian approximate the reduced density matrix with the limited accuracy of its pair of eigenstates with the largest weight. As the adiabatic approximation becomes more accurate with decreasing excitation energy, the probability distribution of the angle of the total angular momentum around a principal axis approaches the one of the full reduced density matrix. The
E2 transition probabilities and spectroscopic quadrupole moments reflect this trend.
Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are exponentially suppressed, as lower-entropy configurations have fewer available microstates and are statistically improbable. However, introducing quantum coherence and structured quantum interference among semiclassical trajectories significantly changes this scenario. Quantum coherence reduces local entropy by establishing correlations among states that are classically independent, effectively restructuring probability amplitudes to channel transitions toward otherwise improbable low-entropy states. We analyze this phenomenon explicitly within the framework of semiclassical approximations, employing the Van Vleck-Gutzwiller propagator to quantify how interference terms arising from coherent superpositions modify classical fluctuation theorems. We demonstrate that quantum coherence, especially when combined with chaos-assisted dynamical tunneling, greatly enhances the probability of transitions to low-entropy configurations, creating pronounced counter-ergodic effects. Furthermore, by considering purification of mixed quantum states, we propose methodologies for deliberately engineering quantum phases among interfering pathways. This phase engineering can explicitly enhance coherence-driven transitions into lower-entropy states, providing a novel thermodynamic resource. Finally, we explore the feasibility of molecular-scale quantum machines exploiting these principles, highlighting their potential applications in quantum thermodynamics and quantum biology for performing useful work through coherence-mediated entropy reduction.