Integrability of Heat and Its Integrating Factor in Classical Thermodynamics(Condensed Matter and Statistical Physics)

概要

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A symmetry called 'scaling' and a transformation accompanying this symmetry are introduced into the thermodynamic state space M using the fourth law of thermodynamics (coined by Landsberg in 1961 for the 'intensive-extensive' dichotomy of thermodynamic variables). Combining the condition stated in Caratheodory's lemma with the transformation 'scaling', the integrating factor β for ω_H is formulated to be given by lnβ(p) - lnβ(p_0) = ln{ω_H(∂_g)_<p0>/ω_H(∂_g)_p} + ∫_c{ω_H/ω_H(∂_g)}, where ω_H denotes the 1-form that expresses heat, ∂_g the infinitesimal transformation of 'scaling', p the point in M, p_0 some fixed point in M, c the path connecting p_0 to p. The entropy function is given by S_p = β(p)ω_H(∂_g)_p. For these two functions to be globally meaningful, the path integral ∫_γ{ω_H/ω_H(∂_g)} vanishes for all elements γ of the Poincare fundamental group.
理論物理学刊行会の論文
2004-08-25