Comment on "Typicality for Generalized Microcanonical Ensemble"

Canonical Typicality

It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for classical distributions on the phase space and for quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subsp…

Generalized Wigner-von Neumann entropy and its typicality

We propose a generalization of the quantum entropy introduced by Wigner and von Neumann in 1929 [Zeitschrift für Physik 57, 30 (1929)]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension $N$ of the Hilbert space is large, as a result of typicality, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of choices of basis and is asymptotically equal to $\ln N$. The dynamic evolution of our entropy is also typical, reminiscent of quantum H theorem proved by von Neumann. For the microcanonical ensemble, the GWvN entropy is equivalent…

量子典型性在非阿贝尔规范约束下幸存：在$SU(2)$格点规范理论中得到精确解析预测验证

Quantum typicality survives non-Abelian gauge constraints: exact analytical prediction confirmed in $SU(2)$ lattice gauge theory

通过$SU(2)$格点规范理论，证明量子典型性在物理希尔伯特空间中仍然成立，并给出无参数解析预测，表明关联增长需要非典型初始条件。

Comments on the paper "Foundation of statistical mechanics from symmetries of entanglement" by S. Deffner and W. Zurek

The authors of the recent paper [1] boldly claim to discover a new fully quantum approach to foundation of statistical mechanics: "Our conceptually novel approach is free of mathematically ambiguous notions such as probability, ensemble, randomness, etc." The aim of this note is to show that this approach is neither specific for quantum systems nor really conceptually different from the standard textbook arguments supporting microcanonical or canonical ensembles in statistical mechanics.