The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a unique determination of the probability distribution (called {\rm SRB} distribution on phase space providing the time averages of the observables. It also implies an expression for a few averages concrete enough to derive consequences of symmetry properties like the fluctuation theorem or to formulate a theory of coarse graining unifying the foundations of equilibrium and of nonequilibrium.
Quantum fluctuations and chaos in fully connected spin models
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院）；Department of Physics, University of Konstanz（康斯坦茨大学物理系）
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究中心国际理论科学中心）；Science, Mathematics and Technology Cluster, Singapore University of Technology and Design（新加坡科技设计大学科学技术集群）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室）
