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Open AccessArticle

The Correlation Production in Thermodynamics

by Sheng-Wen Li 1,2
1
Center for Quantum Technology Research, School of Physics, Beijing Institute of Technology, Beijing 100081, China
2
Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA
Entropy 2019, 21(2), 111; https://doi.org/10.3390/e21020111
Received: 21 December 2018 / Revised: 18 January 2019 / Accepted: 20 January 2019 / Published: 24 January 2019
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other. View Full-Text
Keywords: thermodynamics; macroscopic irreversibility; microscopic reversibility; entropy production; mutual information; correlation production thermodynamics; macroscopic irreversibility; microscopic reversibility; entropy production; mutual information; correlation production
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Li, S.-W. The Correlation Production in Thermodynamics. Entropy 2019, 21, 111.

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