Datta Sandip, Sharma Ashutosh, Ramaswamy Ramakrishna
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036104. doi: 10.1103/PhysRevE.68.036104. Epub 2003 Sep 10.
The thermodynamic formalism is applied to dynamical attractors which have fractal geometry and on which all Lyapunov exponents are exactly zero. Such critical strange nonchaotic attractors (SNAs) which arise, for example, in the Harper system exhibit a static phase transition in the free energy. The Tsallis nonextensive entropy which is known to characterize the thermodynamics of systems with leading Lyapunov exponent zero is found to be subadditive for the critical states. These properties are shared by other quasiperiodic systems with critical SNAs.
热力学形式主义被应用于具有分形几何且所有李雅普诺夫指数恰好为零的动力学吸引子。例如，在哈珀系统中出现的这种临界奇异非混沌吸引子（SNA）在自由能中表现出静态相变。已知用于表征主导李雅普诺夫指数为零的系统热力学的Tsallis非广延熵对于临界状态是次可加的。这些性质也为其他具有临界SNA的准周期系统所共有。
