Thermodynamic Geometry in the Quantum Many-body Problem

Robert Rode

We propose a discrete holographic framework for analyzing the thermodynamic origins of classical chaos in the three-body problem. By representing interacting point masses as localized Bekenstein horizons on a unitary MERA tensor network, we propose that classical Lyapunov divergence is an emergent kinematic projection of epistemic coarse-graining. At the discrete zero-dissipation limit, Node Symmetry Invariance (NSI) dictates strictly unitary evolution and exact Poincaré recurrence. The mapping of this network into a continuous macroscopic phase space requires the continuous truncation of Schmidt coefficients due to the Coffman-Kundu-Wootters (CKW) monogamy bound of tripartite entanglement. By invoking Pesin's Identity, we mathematically map the observed continuous Lyapunov exponent directly to the thermodynamic integration of this Landauer boundary erasure over time. Finally, we demonstrate that the fractal geometries of macroscopic strange attractors correspond to generalized Ryu-Takayanagi minimal surfaces, indicating that chaotic orbits are thermodynamic geodesics minimizing the continuous projection of discrete quantum noise.

John Goold

Israel Michael Sigal

Akshay Krishna, Matteo Ippoliti, R. N. Bhatt

We explore the problem of localization in topological and nontopological nearly-flat subbands derived from the lowest Landau level, in the presence of quenched disorder and short-range interactions. We consider two models: a suitably engineered periodic potential and randomly distributed pointlike impurities. We perform numerical exact diagonalization on a torus geometry and use the mean level spacing ratio $\ensuremath{\langle}r\ensuremath{\rangle}$ as a diagnostic of ergodicity. For topological subbands, we find there is no ergodicity breaking in both the one- and two-dimensional thermodynamic limits. For nontopological subbands, in contrast, we find evidence of an ergodicity breaking transition at finite disorder strength in the one-dimensional thermodynamic limit. Intriguingly, indications of similar behavior in the two-dimensional thermodynamic limit are found as well. This constitutes a novel, continuum setting for the study of the many-body localization transition in one and two dimensions.

Walter Greiner

Joshua Eglinton, Tuomas Pyhäranta, Keiji Saito +1 more

Abstract Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the Bose–Einstein condensate-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model (Myers et al 2022 New J. Phys. 24 025001). Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.