Nonlinear effect of nonequilibrium fluctuations and mesoscopic models

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K05196
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Ibaraki University
• Principal Investigator: Nakagawa Naoko 茨城大学, 理工学研究科(理学野), 教授 (60311586)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 非平衡定常状態 / 大域温度 / 変分原理 / 過冷却状態の安定化 / 粗視化ダイナミクス / ランジュバン方程式

Outline of Final Research Achievements

First, we derive coarse-grained dynamics in nonequilibrium steady states for a model defined in a microscopic description. It is shown that the dynamics after coarse-graining does not provide the true amount of energy dissipation. Second, we identify that a new type of the Langevin equation which reproduces a directional Brownian motion in a Rayleigh piston driven by a temperature difference.
Third, numerical measurements of non-equilibrium entropy are performed for heat conduction systems, where the additivity undoes the extensivity in entropy. Then, we propose global temperature for the whole heat conduction system, which leads to thermodynamic frameworks and variational principle for heat conduction systems. It is predicted that the supercooled states, which are unstable in equilibrium, become stabilized by the heat flow.

Free Research Field

非平衡熱力学

Academic Significance and Societal Importance of the Research Achievements

メゾスコピックレベルの観測結果だけからエネルギー収支はわからないという結論は、今後のメゾスコピックマシンの研究のあり方に影響を及ぼす。平衡ブラウン運動を記述する方程式を非平衡ブラウン運動に素朴に拡張適用できないとの結論は、新しい方程式の簡潔な形式とともに、非平衡ブラウン運動についての新しい研究の必要性を示す。非平衡定常系全体を特徴付ける大域温度、およびそれに基づく変分原理から得られた予言が実験的に検証されれば、過冷却状態の安定化という未知の現象が解明され、様々な非平衡現象に新しい方法論を提供することができる。