科研之友
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摘要
We review two definitions of temperature in statistical mechanics, T-B and T-G, corresponding to two possible definitions of entropy, S-B and S-G, known as surface and volume entropy respectively. We limit our attention to a class of systems with bounded energy, and such that the second derivative of S-B, with respect to energy, is always negative. The second condition holds in systems where the number N of degrees of freedom is sufficiently large (examples are shown where N similar to 100 is sufficient) and without long-range interactions. We first discuss the basic role of T-B, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how T-B can be measured dynamically, i.e. averaging over a single long experimental trajectory. The same approach cannot be used in a generic system for T-G, since the equipartition theorem may be impaired by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small S-B, or equivalently at small vertical bar T-B vertical bar, depends on the sign of T-B.
- 出版日期2015-12
