TY - JOUR
T1 - Emergent entropy production and hydrodynamics in quantum many-body systems
AU - Banks, Tom
AU - Lucas, Andrew
N1 - Funding Information: We thank Mukund Rangamani and Steve Shenker for helpful discussions. A.L. is supported by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4302. Publisher Copyright: © 2019 American Physical Society.
PY - 2019/2/6
Y1 - 2019/2/6
N2 - We study the 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 nonhydrodynamic 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.
AB - We study the 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 nonhydrodynamic 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.
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U2 - https://doi.org/10.1103/PhysRevE.99.022105
DO - https://doi.org/10.1103/PhysRevE.99.022105
M3 - Article
C2 - 30934247
VL - 99
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 2
M1 - 022105
ER -