Emergent entropy production and hydrodynamics in quantum many-body systems

TL;DR

This paper demonstrates how energy dynamics in ergodic quantum many-body systems can be effectively described by classical hydrodynamics, revealing emergent entropy production and providing a framework for deriving quantum hydrodynamics rigorously.

Contribution

It introduces a coarse-grained, classical diffusion equation for energy configurations in quantum systems, establishing a link between microscopic quantum dynamics and macroscopic hydrodynamics.

Findings

Energy dynamics are well approximated by a classical diffusion equation.

Absence of non-hydrodynamic slow modes in the system.

Observable entropy obeys the local second law of thermodynamics.

Abstract

We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy. This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime. We find the absence of non-hydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium. The observable part of the microscopic entropy obeys the local second law of thermodynamics, and quantitatively agrees with the phenomenological predictions of hydrodynamics. Our approach naturally generalizes to ergodic systems with additional symmetries, may lead to numerical algorithms to calculate diffusion constants for lattice models, and implies sufficiency conditions for a rigorous derivation of hydrodynamics in quantum systems.