Derivation of Hydrodynamics from the Hamiltonian description of particle systems

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.Comment: 7 pages. Minor revisions are made in ver.2; In ver.3, the presentation has been revised substantially, and this version will be published in Phys. Rev. Let

Computation of the Kolmogorov-Sinai entropy using statistitical mechanics: Application of an exchange Monte Carlo method

We propose a method for computing the Kolmogorov-Sinai (KS) entropy of chaotic systems. In this method, the KS entropy is expressed as a statistical average over the canonical ensemble for a Hamiltonian with many ground states. This Hamiltonian is constructed directly from an evolution equation that exhibits chaotic dynamics. As an example, we compute the KS entropy for a chaotic repeller by evaluating the thermodynamic entropy of a system with many ground states.Comment: 7 page

Numerical simulations on Szilard's engine and information erasure

We present a computational model for Szilard's engine and the information discarding process. Taking advantage of a fact that the one is essentially the reversed cycle of the other, we can discuss the both by employing the same model. Through numerical simulations we calculate the work extracted by the engine and the heat generation in the information discarding process. It is found that these quantities depend on some realistic ingredients, which means that the work done by the engine is no longer canceled by the heat generation in the information erasure.Comment: 8 pages, 6 figures. submitted to Phys. Rev. Let