What it takes to shun equilibration

Abstract

Numerous works have shown that under mild assumptions unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states and show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system which itself has a large resilience. In this way, we establish a new link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches and investigate the (im-)possibility of formulating a second law of equilibration, by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.

6 pages + 4 pages of Supplemental Material

References in corpus (10)

• Reference frames, superselection rules, and quantum information
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Entanglement Theory and the Second Law of Thermodynamics
• Structure of the resource theory of quantum coherence
• Equilibration time scales in closed many-body quantum systems
• Markovian evolution of quantum coherence under symmetric dynamics
• Towards local equilibration in closed interacting quantum many-body systems

Cited by in corpus (8)

• Entanglement-ergodic quantum systems equilibrate exponentially well
• Equilibration towards generalized Gibbs ensembles in non-interacting theories
• Relaxation, chaos, and thermalization in a three-mode model of a BEC
• Equilibration times in closed quantum many-body systems
• Entanglement production by interaction quenches of quantum chaotic subsystems
• Equilibration on average in quantum processes with finite temporal resolution
• Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
• Equilibration of Isolated Systems: investigating the role of coarse-graining on the initial state magnetization