The aim of the present interdisciplinary review is to carry out a comparative analysis of the notions of thermodynamic entropy, information entropy and entropy of non-equilibrium states and flow of entropy from a critical perspective. The problems of temporal evolution and time directionality are discussed in this context as well. The interrelation of these notions is studied with focusing on the non-equilibrium entropy. The paper is aimed to clarify the notion of entropy, entropy production and its generalizations. The Boltzmann, Gibbs, von Neumann, Shannon, Renyi, Tsallis and others types of entropy are considered concisely. The notions of the steady state, local state and local equilibrium are analyzed thoroughly to expose similarities and dissimilarities of various approaches to the definition of the entropy of nonequilibrium states. The extremal principles for entropy and entropy production are analyzed and discussed in this connection. The purpose of the present study is to elucidate certain aspects of the non-equilibrium statistical mechanics, namely the principal role of the correct description of the temporal evolution of a system and the corresponding procedure of averaging. We also touch tersely the intriguing problems of directionality of time and causality as well as relevance of constructal law that accounts for the phenomenon of evolution.

中文翻译：

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时间演变，时间方向性和不可逆性

本跨学科综述的目的是从批判性角度对热力学熵，信息熵和非平衡态的熵以及熵流的概念进行比较分析。在这种情况下，还讨论了时间演化和时间方向性的问题。这些概念的相互关系着眼于非平衡熵。本文旨在阐明熵，熵产生及其概括的概念。简洁地考虑了玻耳兹曼，吉布斯，冯·诺依曼，香农，人意，沙利斯和其他类型的熵。对稳态，局部状态和局部平衡的概念进行了详尽的分析，以揭示定义非平衡态熵的各种方法的异同。在这方面，对熵和熵产生的极值原理进行了分析和讨论。本研究的目的是阐明非平衡统计力学的某些方面，即正确描述系统的时间演化以及相应的平均过程的主要作用。我们还简要地探讨了时间和因果关系的方向性的有趣问题，以及解释进化现象的建构法则的相关性。即正确描述系统时间演化及其平均过程的主要作用。我们还简要地探讨了时间和因果关系的方向性的有趣问题，以及解释进化现象的建构法则的相关性。即正确描述系统时间演化及其平均过程的主要作用。我们还简要地探讨了时间和因果关系的方向性的有趣问题，以及解释进化现象的建构法则的相关性。