Related papers: Revisiting the Mazur bound and the Suzuki equality
Rigorous lower bound on the time-average of the autocorrelation function of an arbitrary L^1 observable is proven in terms of conserved quantities and ergodic decompositions of the Hamiltonian dynamics. Improvements with respect to the…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal…
We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality (FRI) and the thermodynamic uncertainty relation (TUR). We show that…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…
We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
We study the two time correlation for the noise driven dynamics of the double-well oscillator in the Suzuki regime. It is seen that for very small noise strength the correaltion function shows a lack of translational invariance for very…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated…
Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these…
The Ford-Kac-Mazur formalism is used to study quantum transport in (1) electronic and (2) harmonic oscillator systems connected to general reservoirs. It is shown that for non-interacting systems the method is easy to implement and is used…
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of…