Second Law of Thermodynamics and Macroscopic Observables within Boltzmann's principle, an attempt

Details Second Law of Thermodynamics and Macroscopic Observables within Boltzmann's principle, an attempt Second Law of Thermodynamics and Macroscopic Observables within Boltzmann's principle, an attempt

2000-11-08

arxiv.org/abs/cond-mat/0011130v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, no figures

Scientific paper

Boltzmann's principleS=k*ln W is generalized to non-equilibrium Hamiltonian systems with possibly fractal distributions in phase space by the box-counting volume. The probabilities P(M) of macroscopic observables M are given by the ratio P(M)=W(M)/W of these volumes of the sub-manifold {M} of the microcanonical ensemble with the constraint M to the one without. With this extension of the phase-space integral the Second Law is derived without invoking the thermodynamic limit. The irreversibility in this approach is due to the replacement of the phase space volume of the possibly fractal sub-manifold {M} by the volume of the closure of {M}. In contrast to conventional coarse graining the box-counting volume is defined by the limit of infinite resolution.

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