Geometrical phase and thermodynamics

Jean Ruiz

Zhaoyu Fei, Yu-Han Ma

Geometric phases are foundational to isolated quantum systems, yet their thermodynamic role in open systems remains unrevealed Developing a dissipative adiabatic perturbation expansion, we discover a Berry-phase-induced chiral work difference that survives decoherence. This chirality evolves from an interferometric thermodynamic Aharonov-Bohm effect in the unitary regime to a fringe-free signal in the dissipative regime. We illustrate this framework in a two-level system and assess its experimental feasibility. Our findings clarify the role of quantum geometry in the geometric formulation of thermodynamics.

Wolfhard Janke E, Adriaan M. J. Schakel

Gang Chen, Juqi Li, J.-Q. Liang

We obtain the ground-state energy level and associated geometric phase in the Dicke model analytically by means of the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field is derived with the time-dependent unitary transformation. It is shown that the quantum phase transition characterized by the nonanalyticity of the geometric phase is remarkably of the first order. We also investigate the scaling behavior of the geometric phase at the critical point, which can be measured in a practical experiment to detect the quantum phase transition.

Ravi Baijulal Bhandari

M. Portesi, Ángel Luis Plastino, F. Pennini

We present, from an information theoretic viewpoint, an analysis of phase transitions and critical phenomena in quantum systems. Our study is based on geometrical considerations within the Riemannian space of thermodynamic parameters that characterize the system. A metric for the space can be derived from an appropriate definition of distance between quantum states. For this purpose, we consider generalized α-divergences that include the standard Kullback–Leibler relative entropy. The use of other measures of information distance is taken into account, and the thermodynamic stability of the system is discussed from this geometric perspective.