Statistical physics and fluctuations in ballistic non-equilibrium systems

In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions-each of them at different temperatures-and there are only few collisions, in such a way that equilibrium between the different populations will be reached very slowly. Here, we tentatively approach the local distribution function by a superposition of local-equilibrium distribution functions with different temperatures, corresponding to the different starting positions of the particles. In a second-order expansion, we find a distribution function which depends not only on the Hamiltonian H but also on H², and we study the additional contribution to energy fluctuations.     

Theory of fluctuations in non-equilibrium Fermi gas

We present the equations for the equal-time two-particle correlation functions in degenerate electron gas. In association with the Onsager-type equation for the time-displaced correlation function, the equations constitute the basis of the theory of fluctuations in non-equilibrium degenerate electron gas. Thanks to the prevalence of the small-angle inter-electron scattering, the theory takes a rather simple form.     

Quantum fluctuations in quantum lattice systems with continuous symmetry

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems atT=0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For one-dimensional systems, it is shown that the ground state is invariant under a continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than|r| ^–d+1 whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice systems having not-too-long-range interactions.     

Small fluctuations in a steady non-equilibrium state

An expression for the probability of fluctuations in a given probability distribution deduced in an earlier paper is used to derive a relation between autocorrelations of velocities and the dynamics of small fluctuations in a stable steady state. The steady state may lie in the region of nonlinear thermodynamics. The considerations are restricted to systems with a distinctly separated behaviour on short and long time scale and the corresponding use of Mori distributions.     

Nonlinear fluctuations around a non-equilibrium asymptotic state

Nonlinear fluctuations, which are observed around a non-equilibrium asymptotic state realized at a minimum point of the K-entropy, have a correlation function with inverse time characteristic exhibiting a low frequency divergence in its special representation.     

Critical behaviour of elastically coupled systems with spatially anisotropic critical fluctuations

The spatial anisotropy of critical fluctuations has strong influence on the temperature dependence of the elastic constants of an elastic medium coupled magneto- or electrostrictive to the order parameter. Under pinned boundary conditions we find for uniaxial dipolar systems of hexagonal and trigonal symmetry a second order phase transition, where only c₁₁ and c₁₂ show critical behaviour. For other symmetries a first order transition is expected. At an uniaxial Lifshitz point only c₃₃ becomes critical and the phase transition remains of second order for any symmetry.     

Particle-particle correlation and fluctuations in non-equilibrium Fermi/Bose gases

A theory of fluctuations and correlations in non-equilibrium Fermi and Bose gases is developed. A specific quantum correlation is predicted in non-equilibrium collisional quasi-classical gases, created by collisions between particles. The expressions for correlation sources entering the equation for an equal-time two-particle correlation function are obtained and analyzed. The expressions are valid for arbitrary particle-particle interaction potentials. The possibility of display of the quantum correlation in the macroscopic characteristics of fluctuation phenomena in non-equilibrium gases (e.g., current fluctuations in semiconductors) is discussed. A comparison with correlations in a Lorentz gas is made.     

A note on non-equilibrium work fluctuations and equilibrium free energies

We consider in this paper, a few important issues in non-equilibrium work fluctuations and their relations to equilibrium free energies. First we show that the Jarzynski identity can be viewed as a cumulant expansion of work. For a switching process which is nearly quasistatic the work distribution is sharply peaked and Gaussian. We show analytically that dissipation given by average work minus reversible work W_R, decreases when the process becomes more and more quasistatic. Eventually, in the quasistatic reversible limit, the dissipation vanishes. However the estimate of p, the probability of violation of the second law given by the integral of the tail of the work distribution from −∞ to W_R, increases and takes a value of 0.5 in the quasistatic limit. We show this analytically employing Gaussian integrals given by error functions and the Callen-Welton theorem that relates fluctuations to dissipation in process that is nearly quasistatic. Then we carry out Monte Carlo simulation of non-equilibrium processes in a liquid crystal system in the presence of an electric field and present results on reversible work, dissipation, probability of violation of the second law and distribution of work.     

Fluctuations and large deviations in non-equilibrium systems

For systems in contact with two reservoirs at different densities or with two thermostats at different temperatures, the large deviation function of the density gives a possible way of extending the notion of free energy to non-equilibrium systems. This large deviation function of the density can be calculated explicitly for exclusion models in one dimension with open boundary conditions. For these models, one can also obtain the distribution of the current of particles flowing through the system and the results lead to a simple conjecture for the large deviation function of the current of more general diffusive systems.     

Work and power production in non-equilibrium systems

We study work production in a Markov system obeying discrete stochastic dynamics. As our main result, we establish a new equality concerning the work produced during a spontaneous transformation in an isothermal, non-equilibrium system. Then we consider the overall evolution of a non-equilibrium system driven by an external parameter and generalize Jarzynski's equality for systems maintained out of equilibrium. That equality is recovered if the initial and final state distributions are equilibriums.     

Critical fluctuations in a random network model

Individual threshold behaviors generate large endogenous fluctuations in a globally interactive network. In a version of NK models, the bonds are allowed to be allocated randomly across nodes in each period. It is shown that the aggregate output asymptotically follows a branching process with martingale property on a unique globally stable state.     

Critical fluctuations in a mesoscopic superconducting ring

The nonlocal magnetoconductivity fluctuations in a superconducting submicron ring, with radius comparable to the Ginzburg-Landau coherence length, are studied. The order parameter mode separation yields to the solution of the time-dependent Ginzburg-Landau equation and the paraconductivity Fourier components are calculated in the vicinity of the critical temperature, including the critical fluctuation region. The homogeneous component has a logarithmic singularity at T(c) while the other components are found to be not singular.