Macroscopic length correlations in non-equilibrium systems and their possible realizations

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 of other intensive quantities q at intermediate times. We demonstrate that at these times, during which the global intensive quantities q vary at a finite rate, the associated covariance, the connected pair correlator Gij = qiqj − qi qj , between any two (far separated) sites i and j in a macroscopic system may, on average, become finite. Such non-vanishing connected correlations between distant sites are general and may also appear in quantum and classical theories that only have local interactions. If in an initial equilibrium state, the intensive quantities q are static then a minimal time scale tmin may need to be exceeded in order for an external drive to create a finite expectation value of dq/dt; concomitantly, in such driven systems, a finite average of Gij over all site pairs can appear at times t > tmin. For systems of linear scale L with a maximal (Lieb-Robinson or other) speed v, this minimal time tmin = O(L/v). Once the global mean q no longer changes, the average of Gij 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 derive uncertainty relation based inequalities that connect the heat capacity to the dynamics in general open thermal systems. These rigorous inequalities suggest the shortest possible fluctuation times scales in open equilibrated systems at a temperature T are typically "Planckian" (i.e., O( /(kBT ))). We briefly comment on parallels between quantum measurements, unitary quantum evolution, and thermalization and on how Gaussian distributions of intensive quantities may generically emerge at long times after the system is no longer driven.

The “glass transition” as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse

“…Thus, having a finite width of the energy density is, essentially, inescapable. This general conclusion may be made vivid by exact calculations on various model systems such as generic Heisenberg ferromagnets or antiferromagnets on arbitrary lattices that are quenched by altering external magnetic fields 54 . The bounds of Eqs.…”

Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems

“…Recent years saw the revival of questions concerning the venerable role of Planck's constant in high temperature systems and a flurry of new hypotheses concerning "Planckian" bounds [4][5][6][7][8][9][10][11][12][13][14][15][16][17] on various physical quantities (including, notably, viscosities, their ratio to the entropy density, heat diffusion, and conductivities). These more recent conjectures were largely triggered by Maldacena's * zohar@wustl.edu celebrated AdS-CFT correspondence [18,19].…”

“…These more recent conjectures were largely triggered by Maldacena's * zohar@wustl.edu celebrated AdS-CFT correspondence [18,19]. These new surmised bounds [4][5][6][7][8][9][10][11][12][13][14][15][16][17] are intimately related to the aptly called "Planckian time scales" (τ P lanck = /(k B T )) multiplying the frequency in expressions for black-body radiation (involving the temperature T of the system, Planck's constant, and the Boltzmann constant (also first introduced by Planck [20])), Einstein's and Debye's subsequent calculations [21,22] of phonon contributions to the heat capacity, and many other arenas. Wigner's "quantum correction" expansion about the classical equilibrium distribution [23] involves powers of Planck's constant multiplied by those of the inverse temperature.…”

“…As fundamental entities, Planckian time scales are pivotal to quantum critical phenomena [27][28][29] as well as various quantum effects, e.g., [30] at finite temperature. Planckian type time scales are also central to numerous questions concerning correlations, equilibration, and information scrambling [7,8,16,[31][32][33][34][35]. The Sachdev-Ye-Kitaev model [36][37][38] and its myriad extensions and applications, e.g., [39][40][41][42][43][44] have made some of these concepts more tangible.…”

Strongly coupled quantum phonon fluid in a solvable model

“…Often, the current relaxation times are tied to extrinsic mechanisms, such as the momentum loss rate due to impurity scattering. However, in setups where the bottleneck for current relaxation is the intrinsic thermalization time in the system, it has been proposed that the relaxation time has to obey a fundamental "Planckian" bound τ th α¯h k B T , where α is an unknown constant of order unity [13,14].…”