We give the explicit structure of the functional governing the dynamical density and current fluctuations for a mesoscopic system in a nonequilibrium steady state. Its canonical form determines a generalised Onsager-Machlup theory. We assume that the system is described as a Markov jump process satisfying a local detailed balance condition such as typical for stochastic lattice gases and for chemical networks. We identify the entropy current and the traffic between the mesoscopic states as extra terms in the fluctuation functional with respect to the equilibrium dynamics. The density and current fluctuations are coupled in general, except close to equilibrium where their decoupling explains the validity of entropy production principles.PACS numbers: 05.70.Ln, Fluctuation theory is at the heart of statistical mechanics. About a century ago appeared the first fluctuation formulae regarding equilibrium systems, in particular from Boltzmann's statistical interpretation of the thermodynamic entropy. As example, the equilibrium density fluctuations of a gas in large volume V at inverse temperature β and chemical potential µ satisfy the asymptotic lawwhere Ω(µ) is the grand potential and Ω(µ, n) = F (n) − µ n with F (n) the free energy, is the corresponding variational functional; at least away from the phase coexistence regime where droplet formation or nucleation mechanisms become responsible for a slower, surfaceexponential decay. Yet in all cases, there appears an important relation between the structure of equilibrium fluctuations and the thermodynamics of the system, making the equilibrium domain exceptionally well understood. In particular, the variational principles characterising equilibrium can be understood as an immediate consequence of its fluctuation theory and response relations can be derived from expanding (1) around the equilibrium density n 0 . In order to include dynamics in the fluctuation theory, Onsager and Machlup derived the generic structure of small time-dependent equilibrium fluctuations and explained how their dynamics relates to the return to equilibrium, [1]. The ensuing linear response theory formalised the general relation between equilibrium current fluctuations and the response in driven systems in a firstorder perturbation theory around equilibrium. To go beyond and challenged by e.g. the fast progress in nonequilibrium experiments on nanoscale, one soon realises a * Electronic address: christian.maes@fys.kuleuven.be † Electronic address: netocny@fzu.cz lack of general principles. Moreover it would be too optimistic to think nonequilibrium physics based solely on quantities typical to equilibrium descriptions supplemented with the corresponding currents. Deeply related to that is the lack of generally valid variational principles for nonequilibrium steady states, beyond the approximate ones of minimum/maximum entropy production. Yet, more recently there has also been great progress. One well-known approach to dynamical (and especially current) fluctuations in open systems adds to the ...

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants ͗͗n m ͘͘ of the number n of passed charges to very high orders (up to m ‫؍‬ 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.cumulants ͉ distributions ͉ electron transport ͉ noise and fluctuations C ounting statistics concerns the probability distribution P n of the number n of random events that occur during a certain time span t. One example is the number of electrons that tunnel through a nanoscopic system (1-4). The first cumulant of the distribution is the mean of n, ͗͗n͘͘ ϭ ͗n͘, the second is the variance, ͗͗n 2 ͘͘ ϭ ͗n 2 ͘ Ϫ ͗n͘ 2 , the third is the skewness, ͗͗n 3 ͘͘ ϭ ͗(n Ϫ ͗n͘) 3 ͘. With increasing order the cumulants are expected to contain more and more detailed information on the microscopic correlations that determine the stochastic process. In general, the cumulants ͗͗n m ͘͘ ϭ S (m) (z ϭ 0) are defined as the mth derivative with respect to the counting field z of the cumulant generating function (CGF) S(z) ϭ ln͚ n P n e nz . Recently, theoretical studies of a number of different systems have found that the high-order cumulants oscillate as functions of certain parameters (5-9), however, no systematic explanation of this phenomenon has so far been given. Examples include oscillations of the high-order cumulants of transport through a Mach-Zender interferometer as functions of the Aharonov-Bohm flux (6), and in transport through a double quantum dot as functions of the energy dealignment between the two quantum dots (8). As we shall demonstrate, oscillations of the high-order cumulants in fact constitute a universal phenomenon which is to be expected in a large class of stochastic processes, independently of the microscopic details. Inspired by recent ideas of M. V. Berry for the behavior of high-order derivates of complex functions (10), we show that the high-order cumulants for a large variety of stochastic processes become oscillatory functions of basically any parameter, including time in the transient regime. We develop the theory underlying this surprising phenomenon and present the first...

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We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibrium. Their decoupling close-to-equilibrium explains the validity of entropy production principles.Comment: rewritten versio