For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a consequence of microreversibility. These relations are systematically deduced from the extension of the fluctuation relation for this class of systems, and analyzed by using methods developed in [M. Barbier and P. Gaspard, J. Phys. A: Math. Theor. 51 (2018) 355001]. We unambiguously identify, among the statistical cumulants and their nonequilibrium responses, which of these quantities are independent and thus left unspecified by the fluctuation relation, i.e. by microreversibility. We also find the explicit expression of the dependent quantities in terms of the independent ones by means of coefficients of Euler polynomials.
Microreversibility constrains the fluctuations of the nonequilibrium currents that cross an open system. This can be seen from the so-called fluctuation relations, which are a direct consequence of microreversibility. Indeed, the latter are known to impose time-reversal symmetry relations on the statistical cumulants of the currents and their responses at arbitrary orders in the deviations from equilibrium. Remarkably, such relations have been recently analyzed by means of Euler's polynomials. Here we show that fluctuation relations can actually be explicitly written in terms of the constant t…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary orders in the deviations from equilibrium obey time-reversal symmetry relations. It is shown that these relations allow us to systematically reduce the amount of independent quantities that need to be measured experimentally or computed theoretically in order to fully characterize the linear and nonlinear transport properties of general open systems. This r…
The consequences of microreversibility for the linear and nonlinear transport properties of systems subjected to external magnetic fields are systematically investigated in Aharonov-Bohm rings connected to two, three, and four terminals. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is expressed in terms of the scattering matrix of these circuits. The time-reversal symmetry relations up to the third responses of the currents and the fourth cumulants are analytically investigated and numerica…
We analytically calculate the cumulant generating function of energy and particle transport in an open 1D Kitaev chain by utilizing the Keldysh technique. The joint distribution of particle and energy currents obeys different fluctuation relations in different regions of the parameter space as a result of $U$(1) symmetry breaking and energy conservation. We discuss the thermoelectricity of the Kitaev chain as a three terminal system and derive an analytical expression of the maximum work power. The response theory up to the second order is explicitly checked, and the result is consistent with …
Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature active matter systems exist in nonequilibrium states. In this paper the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collect…
We study the stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency larger than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) is illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We disc…
We show that the nonequilibrium response of Markovian dynamics can be made fully symmetric, both near and far from equilibrium. This is achieved by varying the affinities along equivalence classes in the space of stochastic dynamics.
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.
The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation process. Namely, we derive the linear response to perturbations of the noise intensity, mapping it onto the quadratic response to a constant small force. The latter, displaying divergent terms, is explicitly regularized with a novel path-integral method. The nonequilibrium equivalents of heat capacity and thermal expansion coefficient are two applications of thi…
We present examples of how time-symmetric kinetic factors contribute to the response either in nonlinear order around equilibrium or in linear order around nonequilibrium. The phenomenology we associate to that so called frenetic contribution are negative differential conductivity, changes in the Einstein relation between friction and noise, and population inversion.
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from unperturbed correlation functions. These correlations contain a novel form of entropy flow due to temperature unbalances, next to the standard entropy flow of stochastic energetics and to complementary time-symmetric dynamical aspects. Our derivation hinges on a time rescaling, which is a key procedure for comparing apparently incommensurable path weights. An intere…
The force on a probe induced by a nonequilibrium medium is in general nongradient. We detail the mechanism of that feature via nonequilibrium response theory. The emergence of nongradient forces is due to a systematic "twist" of the excess frenesy with respect to the entropy flux, in response to changes in the coupling or in the position of the probe in the nonequilibrium medium.
Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far from equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many body systems. It is illustrated in a four state model and in the near critical Ising model.
Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics
School of Physics, Korea Institute for Advanced Study（韩国高等科学研究院物理学院）；Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University（首尔大学物理与天文学系及理论物理中心）；Quantum Universe Center, Korea Institute for Advanced Study（韩国高等科学研究院量子宇宙中心）
Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this …
A recent experiment driving colloids electromagnetically, by Bérut et al. [2014 Europhys. Lett. 107, 60004], is an ideal paradigm for illustrating a linear response theory for nonequilibrium overdamped systems including hydrodynamic interactions and, unusually, a reservoir itself out of equilibrium. Indeed, in this setup one finds a nonequilibrium environment in which the mobility and diffusivity of free particles are not simply proportional to each other. We derive both the response to a mechanical forcing and to temperature variations in terms of correlations between an observable and a path…
Excess work is a non-diverging part of the work during transition between nonequilibrium steady states (NESSs). It is a central quantity in the steady state thermodynamics (SST), which is a candidate for nonequilibrium thermodynamics theory. We derive an expression of excess work during quasistatic transitions between NESSs by using the macroscopic linear response relation of NESS. This expression is a line integral of a vector potential in the space of control parameters. We show a relationship between the vector potential and the response function of NESS, and thus obtain a relationship betw…
We present a theoretical framework to analyze the violation of fluctuation-response relation (FRR) for any observable from a finite Markov system with two well-separated time scales. We find that, generally for both slow and fast observables, a broad plateau exists in the intermediate frequency region, which contributes to a finite hidden entropy production. Assuming that non-equilibrium behavior arises only from coupling of slow and fast processes, we find that, at large observation time scae, the effective temperature for a slow observable deviates only slightly from the bath temperature, ac…
Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare …
Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from time-symmetric PCA, satisfying detailed balance, and we give their Kubo formula for linear response. Close-to-detailed balance we investigate the form of the McLennan distribution and the minimum entropy production principle. More generally, when time-symmetry is broken in the stationary process, there is a fluctuation symmetry for a corresponding entropy fl…
We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation dissipation relation between friction and noise for probe m…
We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the s…
We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the noncommutativity of quantum operators and establish links to the Kubo response theory for closed quantum systems. We show in particular that the equilibrium response vanishes for perturbations that commute with the unperturbed Hamiltonian while the steady-state response does not, highlighting the profound difference between the two.
