Orbital measures in non-equilibrium statistical mechanics: the Onsager relations

We assume that the properties of nonequilibrium stationary states of systems of particles can be expressed in terms of weighted orbital measures, i.e. through periodic orbit expansions. This allows us to derive the Onsager relations for systems of $N$ particles subject to a Gaussian thermostat, under the assumption that the entropy production rate is equal to the phase space contraction rate. Moreover, this also allows us to prove that the relevant transport coefficients are not negative. In the appendix we give an argument for the proper way of treating grazing collisions, a source of possible singularities in the dynamics.Comment: LaTeX, 14 pages, 1 TeX figure in the tex

The total nucleon-nucleon cross section at large N_c

It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD, the total nucleon-nucleon cross section is independent of incident momentum and given by $\sigma^{\rm total}=2 \pi \log^2(N_c) / (m^2_{\pi})$. This result is valid in the extreme large $N_c$ regime of $\log(N_c) \gg 1$ and has corrections of relative order $\log (\log(N_c))/\log(N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.Comment: 4 page

Nitramine propellants

Nitramine propellants without a pressure exponent shift in the burning rate curves are prepared by matching the burning rate of a selected nitramine or combination of nitramines within 10% of burning rate of a plasticized active binder so as to smooth out the break point appearance in the burning rate curve

Note on Phase Space Contraction and Entropy Production in Thermostatted Hamiltonian Systems

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas.Comment: 16 pages including 1 table and 3 figures. LaTeX forma

Gibbs entropy and irreversible thermodynamics

Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct connection between dynamics and Irreversible Thermodynamics has been claimed to have been found. However, the main quantity used in these studies is a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its present form, to characterize nonequilibrium states. Various simplified models have also been devised to give explicit examples of how the coarse-grained approach may succeed in giving a full description of the Irreversible Thermodynamics. We analyze some of these models pointing out a number of difficulties which, in our opinion, need to be overcome in order to establish a physically relevant connection between these models and Irreversible Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2