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arXiv · 2205.05863

Quasi-static decomposition and the Gibbs factorial in small thermodynamic system

Shin-ichi Sasa·Ken Hiura·Naoko Nakagawa·Akira Yoshida
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Abstract

For small thermodynamic systems in contact with a heat bath, we determine the free energy by imposing the following two conditions. First, the quasi-static work in any configuration change is equal to the free energy difference. Second, the temperature dependence of the free energy satisfies the Gibbs-Helmholtz relation. We find that these prerequisites uniquely lead to the free energy of a classical system consisting of $N$-interacting identical particles, up to an additive constant proportional to $N$. The free energy thus determined contains the Gibbs factorial $N!$ in addition to the phase space integration of the Gibbs-Boltzmann factor. The key step in the derivation is to construct a quasi-static decomposition of small thermodynamic systems.

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Shin-ichi Sasa, Ken Hiura, Naoko Nakagawa, Akira Yoshida. 2022-05-12. Quasi-static decomposition and the Gibbs factorial in small thermodynamic system. https://doi.org/10.1007/s10955-022-02991-7

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