An exact expression for the finite frequency response of open classical systems coupled to reservoirs is obtained. The result is valid for any conserved current. No assumption is made about the reservoirs apart from thermodynamic equilibrium. At non-zero frequencies, the expression involves correlation functions of boundary currents and cannot be put in the standard Green-Kubo form involving currents inside the system.
In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a multi-dimensional linear Markov process. It is shown that the fluctuation-response formalism can be used both to find the direct causal links between the variables of a system and to introduce a degree of causation, cumulative in time, whose physical interpretation is straightforward. Although for generic non-linear dynamics there is no simple exact relationship betwee…
The Carnot theorem, one expression of the second law of thermodynamics, places a fundamental upper bound on the efficiency of heat engines operating between two heat baths. The Carnot theorem can be stated in a more generalized form for heat engines operating with multiple heat baths, where the maximum efficiency is achieved for reversible heat engines operating quasistatically between two heat baths. In this study, we determine the irreversible efficiency of heat engines operating with multiple heat baths in a linear response regime, i.e., under small temperature differences and a slow variat…
Fluctuation-dissipation relations outside the linear response regime in a two-dimensional driven lattice gas along the direction transverse to the driving force
The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation strength to correlations of entropy production of lower order, thereby extending the fluctuation-dissipation-theorem to cases far from equilibrium in a thermodynamic way. The relation is validated and studied for a 4-state-model.
Input and output current fluctuations in stationary cross-transport systems with two kinds of currents are investigated. In Saryal {\it et al.} [Phys. Rev. Lett. 127, 190603 (2021)], upper bounds on input and output current fluctuations are proven in the linear response regime and suggested the validity beyond the linear response regime. We examine these bounds beyond the linear response regime and find that these bounds are violated in general nonequilibrium stationary conditions. We show two examples to demonstrate the violation. Through these examples, we argue that no upper bound on input …
The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscop…
In general, linear response theory expresses the relation between a driving and a physical system's response only to first order in perturbation theory. In the context of charge transport, this is the linear relation between current and electromotive force expressed in Ohm's law. We show here that, in the case of the quantum Hall effect, all higher order corrections vanish. We prove this in a fully interacting setting and without flux averaging.
We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We ident…
We relate explicitly the adiabatic curvature -- in flux space -- of an interacting Hall insulator with nondegenerate ground state to various linear response coefficients, in particular the Kubo response and the adiabatic response. The flexibility of the setup, allowing for various driving terms and currents, reflects the topological nature of the adiabatic curvature. We also outline an abstract connection between Kubo response and adiabatic response, corresponding to the fact that electric fields can be generated both by electrostatic potentials and time-dependent magnetic fields. Our treatmen…
In a recent Letter, Dornheim et al. [PRL 125, 085001 (2020)] have investigated the nonlinear density response of the uniform electron gas in the warm dense matter regime. More specifically, they have studied the cubic response function at the first harmonic, which cannot be neglected in many situations of experimental relevance. In this work, we go one step further and study the full spectrum of excitations at the higher harmonics of the original perturbation based on extensive new ab initio path integral Monte Carlo (PIMC) simulations. We find that the dominant contribution to the density res…
Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are known analytically, and most experiments operate. This allows us to compare the optimal processes obtained in linear response and address their relevance to experiments, using realistic parameter values from experiments with optical tweezers. Our results help assess the accuracy of perturbative methods in calculating the irreversible work for cases where an e…
