2007 Fiscal Year Final Research Report Summary
Microscopic Foundation of Nonequilibrium Thermodynamics of Muticomonent Fluids and Nonlinear Fluctuation
| Project/Area Number |
17540362
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | International Christian University |
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Principal Investigator |
KITAHARA Kazuo International Christian University, Department of Material Science, Professor (20107692)
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| Co-Investigator(Kenkyū-buntansha) |
KITAHARA Kazuo International Christian University, Department of Material Science, Professor (20107692)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Nonequilibrium / Thermodynamics / Statistical mechanicsc / Nonlinear / Fluctuation / Fluid / Multicomponent system / Proiection operator |
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| Research Abstract |
In order to formulate nonequilibrium thermodynamics of multi-component fluids in a unified frame with entropy concept, we introduced Zubarev's projection operator in the microscopic Liouville equation and derived the general formula for reversible part of the evolution of thermodynamic variables ; here "reversible" implies no entropy production. This general formula consists of anti-symmetric matrix and intensive parameters. Thus it automatically explains no entropy production. Namely, the anti-symmetric matrix is the ensemble average of Poisson's bracket of microscopic dynamical variables with respect to nonequilibrium local equilibrium. We have derived evolution equation for one-component fluids completely. However, for multi-component fluids, equations for reversible parts are obtained in compact forms for mass density and momentum density but we obtained very complicated equations, which are not closed within thermodynamic variables. We need further investigation. We also derived L
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angevin-type equations for physical quantities by the usage of projection operator, which is complement to Zubarev's projection operator. It should be mentioned that while the Liouville equation for the distribution function is linear, equations for, physical quantities are non-linear so that there is essential difficulty of difference between the average of a function and the function of the average. Therefore, the projection operator for the physical quantity should be formulated to give linearized equations correctly.
Also we studied the path probability of fluctuation on the basis of path integral. We then derive the ratio of the probability of the evolution of a fluctuation and the probability of its time-reversed fluctuation. It turns out that the ratio is precisely related to the entropy production. Furthermore, we studied fluctuation in a far-from-equilibrium condition such as oscillatory chemical reactions. In this case, we can find that fluctuation along the direction of macroscopic oscillatory direction is more probable than fluctuation with reversed direction. This may be comparable to 'Fluctuation theorem". Less
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Research Products
(8 results)
