Non-Hamiltonian Equilibrium Statistical Mechanics

In this paper the equilibrium statistical mechanics of non-Hamiltonian systems is formulated introducing an algebraic bracket. The latter defines non-Hamiltonian equations of motion in classical phase space according to the approach introduced in Phys. Rev. E 64, 056125 (2001). The Jacobi identity is no longer satisfied by the generalized bracket and as a result the algebra of phase space functions is not time translation invariant. The presence of a nonzero phase space compressibility spoils also the time-reversal invariance of the dynamics. The general Liouville equation is rederived and the properties of statistical averages are accounted for. The features of time correlation functions and linear response theory are also discussed.