Macroscopic Length Correlations in Non-Equilibrium Systems and Their Possible Realizatons

Abstract

We consider general systems that start from and/or end in thermodynamic equilibrium while experiencing a finite rate of change of their energy density or other intensive quantities $q$ at intermediate times. We demonstrate that at these times, during which $q$ varies at a finite rate, the associated covariance, the connected pair correlator $G_{ij}=⟨q_i{q}_j⟩-⟨q_i⟩⟨q_j⟩$, between any two (far separated) sites $i$ and $j$ in a macroscopic system may, on average, become finite. Once the global mean $q$ no longer changes, the average of $G_{ij}$ over all site pairs $i$ and $j$ may tend to zero. However, when the equilibration times are significant (e.g., as in a glass that is not in true thermodynamic equilibrium yet in which the energy density (or temperature) reaches a final steady state value), these long range correlations may persist also long after $q$ ceases to change. We explore viable experimental implications of our findings and speculate on their potential realization in glasses (where a prediction of a theory based on the effect that we describe here suggests a universal collapse of the viscosity that agrees with all published viscosity measurements over sixteen decades) and non-Fermi liquids. We discuss effective equilibrium in driven systems and derive uncertainty relation based inequalities that connect the heat capacity to the dynamics in general open thermal systems. These rigorous thermalization inequalities suggest the shortest possible fluctuation times scales in open equilibrated systems at a temperature $T$ are typically "Planckian" (i.e., $\mathcal{O}(\hslash /(k_{B}T))$). We briefly comment on parallels between quantum measurements, unitary quantum evolution, and thermalization and on how Gaussian distributions may generically emerge.

145 pages, 7 figures (increase in page number primarily due to new style file)

References in corpus (34)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Theoretical perspective on the glass transition and amorphous materials
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Theory of Intertwined Orders in High Temperature Superconductors
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems: Work is not an observable
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Breakdown of thermalization in finite one-dimensional systems
• Theory of universal incoherent metallic transport
• Rise and fall of hidden string order of lattice bosons
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Electronic phase separation in the slightly underdoped iron pnictide superconductor Ba(1-x)K(x)Fe(2)As(2)
• General entanglement scaling laws from time evolution
• The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
• Possible experimental manifestations of the many-body localization
• Calorimetric glass transition explained by hierarchical dynamic facilitation
• Generalization of von Neumann's Approach to Thermalization
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Insights into glass formation and glass transition in supercooled liquids, by study of related phenomena in crystals
• On the stability of many-body localization in $d>1$
• Similar glassy features in the NMR response of pure and disordered La1.88Sr0.12CuO4
• Lieb-Robinson bounds and the speed of light from topological order
• Operator scrambling and quantum chaos
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• A phase space approach to supercooled liquids and a universal collapse of their viscosity
• Non-equilibrium systems have steady-state distributions and non-steady dynamics
• Chaos and thermalization in small quantum systems
• An Extension of ETH to Non-Equilibrium Steady States
• Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
• On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

Cited by in corpus (6)

• Planckian Dissipation in Metals
• On the Planckian bound for heat diffusion in insulators
• Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
• Strongly coupled quantum phonon fluid in a solvable model
• Quantum acoustics unravels Planckian resistivity
• Quantum measurements and equilibration: the emergence of objective outcomes via entropy maximisation