Operational extension of thermodynamic functions for non-equilibrium structure formation

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K03647
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Ibaraki University
• Principal Investigator: Naoko Nakagawa 茨城大学, 理工学研究科(理学野), 教授 (60311586)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 大域熱力学 / 非平衡エントロピー / 準安定状態 / 熱流 / 混合自由エネルギー / Jarzynski等式

Outline of Final Research Achievements

We developed "global thermodynamics" as a new framework for describing macroscopic systems exposed to heat flow, and succeeded in extending the thermodynamic structure to the heat conduction state. By using the variational principle in accordance with this framework, we proposed a new phenomenon that "heat flow stabilizes a supercooled gas near the gas-liquid interface". We derived that the entropy in heat conduction systems involves an additional term that leads to nonadditivity. We set up the variational principle of global thermodynamics for multiple environmental settings and confirmed that the states of maximum entropy and minimum free energy are the same nonequilibrium steady state. In addition, we derived a formula for determining the mixing free energies of binary fluids in numerical simulations. The formula reproduced the characteristics of the liquid-gas transition observed in the argon-krypton mixture.

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Free Research Field

非平衡統計力学

Academic Significance and Societal Importance of the Research Achievements

熱力学や統計力学は物性研究の根幹をなし、特に変分原理は平衡での構造予測を可能にする有用性の高い理論である。これらを非平衡状態に拡張する研究は100年以上にわたる歴史がある。大域熱力学は熱伝導系の全体量だけを用いる簡便な記述法だが、非自明な現象予測をもたらすことができ、数値実験による実証例も報告された(PRL, 2023)。大域熱力学が予言する「熱流による準安定状態の制御」はこれまで検討されなかった制御技術と物性開発の新しい可能性を示唆する。また、混合自由エネルギーを数値実験で決定するための新公式は、微小サイズ溶液の潜在能力を数値実験で定量化する新しい方法論を与える。