We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrodinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.
We explore the effects of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a two level system. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing parameters. The odd and even cumulants saturate at two different but uniq…
We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating the first four current cumulants in a nonequilibrium stationary state at high energies, we find that the first two cumulants scale with the system size in a diffusive way, while the 3rd and the 4th cumulants do not. This means that the model is not an ordinary diffusive spin conductor.
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,…
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…
Quantum jump correlations in long-range dissipative spin systems via cluster and cumulant expansions
Scuola Superiore Meridionale（南方高等学院）；SISSA（国际高等研究院）；CNRS, Collège de France（法国国家科学研究中心，法兰西公学院）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques（巴黎西岱大学，法国国家科学研究中心，材料与量子现象研究所）；Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”（那不勒斯费德里科二世大学，E. Pancini物理系）；Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（皮塔耶夫斯基玻色-爱因斯坦凝聚中心，意大利国家研究委员会光电子学与纳米技术研究所，特伦托大学物理系）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所，特伦托基础物理与应用研究所）
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…
We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperatur…
We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at $t=0$. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quan…
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…
The Ziff-Gulari-Barshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. In particular, it exhibits a nonequilibrium, discontinuous transition between a reactive and a CO poisoned phase. If one allows a nonzero rate of CO desorption ($k$), the line of phase transitions terminates at a critical point ($k_{c}$). In this work, instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide (CO$_{2}$) only when they are adsorbed in close proximity, we con…
Recently, some general relations have been studied in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a universal internal relation among the cumulants of currents and the entropy production. In this paper, we give a simple derivation of TUR for thermally fluctuating particle current in a tilted periodic potential from a coarse grained point of view with the use of the transition probabilities. Also, we explore the condition for the bound of TUR to monotonically increase with the affinity.
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a rigorous thermodynamic description of coarse-grained memory systems. In the nearly-quasistatic limit, logically irreversible operations can be performed with thermodynamic reversibility. Yet, here we show that beyond the reversible work Landauer's bound requires of computation, dissipation must be incurred both for modular computation and for neglected stat…
We consider numerical methods for thermodynamic sampling, i.e. computing sequences of points distributed according to the Gibbs-Boltzmann distribution, using Langevin dynamics and overdamped Langevin dynamics (Brownian dynamics). A wide variety of numerical methods for Langevin dynamics may be constructed based on splitting the stochastic differential equations into various component parts, each of which may be propagated exactly in the sense of distributions. Each such method may be viewed as generating samples according to an associated invariant measure that differs from the exact canonical…
Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories, and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related…
Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces
The notion of a nonequilibrium heat capacity is important for bio-energetics and for calorimetry of active materials more generally. It centers around the notion of excess heat or excess work dissipated during a quasistatic relaxation between different nonequilibrium conditions. We give exact results for active random walks moving in an energy landscape on a graph, based on calculations employing the matrix-tree and matrix-forest theorems. That graphical method applies to any Markov jump process under the physical condition of local detailed balance, and is not restricted to the examples given…
The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The …
