On a Definition of Temperature in Equilibrium and Nonequilibrium Systems

We combine the definition of temperature for an Hamiltonian dynamical system, with the Hamiltonian representation of a nonequilibrium isokinetic steady state, to obtain an expression for the temperature away from equilibrium. Results of numerical simulations performed to assess the validity of this approach for color field systems are reported. A strong correlation between the kinetic temperature orthogonal to the color current and the ratio of the averages of two given phase variables is observed. Introduction In a recent paper by Rugh [1], a method of determining the temperature in an hamiltonian dynamical system was proposed. It begins with the definition of the entropy S as the (canonically invariant) weighted area of the energy surface Ω(the level set of the Hamiltonian H(q,p)), under the assumption that the dynamical system is ergodic in Ω. Defining the temperature T(E) in the usual thermodynamic way through 1 T(E) = dS dE , (1) Rugh defines the phase variable Ψ(Γ) = ∂ ∂Γ ⋅ ∂H ∂Γ ∂H ∂Γ ⋅ ∂H ∂Γ 