The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium

Details The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium

2003-10-24

arxiv.org/abs/cond-mat/0310575v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures. Submitted to PRL

Scientific paper

10.1103/PhysRevLett.92.050602

We investigate, via computer simulations, the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables $M$ describing the system are the (empirical) particle density $f=\{f(\un{x},\un{v})\}$ and the total energy $E$. We find that $S(f_t,E)$ is monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of $S(M_t) = S(M_{X_t})$ should hold generally for ``typical'' (the overwhelming majority of) initial microstates (phase-points) $X_0$ belonging to the initial macrostate $M_0$, satisfying $M_{X_0} = M_0$. This is a direct consequence of Liouville's theorem when $M_t$ evolves autonomously.

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