151 research outputs found
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
Equality connecting energy dissipation with violation of fluctuation-response relation
In systems driven away from equilibrium, the velocity correlation function
and the linear response function to a small perturbation force do not satisfy
the fluctuation-response relation (FRR) due to the lack of detailed balance in
contrast to equilibrium systems. In this Letter, an equality between an extent
of the FRR violation and the rate of energy dissipation is proved for Langevin
systems under non-equilibrium conditions. This equality enables us to calculate
the rate of energy dissipation by quantifying the extent of the FRR violation,
which can be measured experimentally.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Lett, v2: major revision,
v3: minor revisio
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