2000/05/15 by T. Kobayashi, Kobayashi, T., Toshiki Shimbori +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum chaos and dynamical systems #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.cond-mat/0005237
openalex publication_date 2000/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Statistical mechanics for states with complex eigenvalues, which are described by Gel'fand triplet and represent unstable states like resonances, are discussed on the basis of principle of equal \it a priori probability. A new entropy corresponding to the freedom for the imaginary eigenvalues appears in the theory. In equilibriums it induces a new physical observable which can be identified as a common time scale. It is remarkable that in spaces with more than 2 dimensions we find out existence of stable and quasi-stable systems, even though all constituents are unstable. In such systems all constituents are connected by stationary flows which are generally observable and then we can say that they are semiclassical systems. Examples for such semiclassical systems are constructed in parabolic potential barriers. The flexible structure of the systems is also pointed out.