Showing papers by "David Ruelle published in 2016"
TL;DR: The asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set is considered, and sufficient criteria is given, involving the location of the zeros of $P(z)$, for these families to satisfy a central limit theorem (CLT) and even a local CLT (LCLT).
46 citations
TL;DR: Given a system M in a thermal bath, a generalized detailed balance relation for the ratio r=πτ(K→J)/πτ (J→K) of the transition probabilities is obtained, where r depends on the amount of heat released to the bath in channel $$\alpha $$α.
Abstract: Given a system M in a thermal bath we obtain a generalized detailed balance relation for the ratio \(r=\pi _\tau (K\rightarrow J)/\pi _\tau (J\rightarrow K)\) of the transition probabilities \(M:J\rightarrow K\) and \(M:K\rightarrow J\) in time \(\tau \). We assume an active bath, containing solute molecules in metastable states. These molecules may react with M and the transition \(J\rightarrow K\) occurs through different channels \(\alpha \) involving different reactions with the bath. We find that \(r=\sum p^\alpha r^\alpha \), where \(p^\alpha \) is the probability that channel \(\alpha \) occurs, and \(r^\alpha \) depends on the amount of heat (more precisely enthalpy) released to the bath in channel \(\alpha \).
7 citations
01 Jan 2016
TL;DR: In this article, it was shown that the macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow in a nonstandard geometry.
Abstract: The hydrodynamic time evolution is Hamiltonian in the inertial range (i.e., in the absence of viscosity). From this we obtain that the macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow in a nonstandard geometry. In the absence of fluctuations this means that the Kolmogorov theory of turbulence is equivalent to a heat flow for a suitable mechanical system. Turbulent fluctuations (intermittency) correspond to thermal fluctuations for the heat flow. A relatively crude estimate of the thermal fluctuations, based on standard ideas of nonequilibrium statistical mechanics is presented: this agrees remarkably well with what is observed in several turbulence experiments. A logical relation with the lognormal theory of Kolmogorov and Obukhov is also indicated, which shows what fails in this theory, and what can be rescued.
1 citations