Statistical Mechanics of Nonequilibrium LiquidsIn recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate-level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration. |
From inside the book
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Page i
... gives a direction to further avenues of exploration. DENIS J. EVANS is Professor of Theoretical Chemistry at the Australian National University (ANU), Dean of the Research School of Chemistry and Convenor of the ANU College of Science ...
... gives a direction to further avenues of exploration. DENIS J. EVANS is Professor of Theoretical Chemistry at the Australian National University (ANU), Dean of the Research School of Chemistry and Convenor of the ANU College of Science ...
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... gives rise to significant inhomogeneities in the thermodynamic properties of the fluid and in the strain rate in particular. This leads to obvious difficulties in the calculation of the shear viscosity. Lees and Edwards (1972), showed ...
... gives rise to significant inhomogeneities in the thermodynamic properties of the fluid and in the strain rate in particular. This leads to obvious difficulties in the calculation of the shear viscosity. Lees and Edwards (1972), showed ...
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... give an exact framework within which one can calculate and characterize transport processes far from equilibrium (Chapter 7). Because of the divergences alluded to above, the nonlinear theory cannot rely on power-series expansions about ...
... give an exact framework within which one can calculate and characterize transport processes far from equilibrium (Chapter 7). Because of the divergences alluded to above, the nonlinear theory cannot rely on power-series expansions about ...
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... give an exact description of the shearing motion of systems arbitrarily far from equilibrium. Again, no Hamiltonian can be found which is capable of generating these equations. When external fields or boundary conditions perform work on ...
... give an exact description of the shearing motion of systems arbitrarily far from equilibrium. Again, no Hamiltonian can be found which is capable of generating these equations. When external fields or boundary conditions perform work on ...
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... gives a simple argument to show that the transport coefficients must be non-negative. The discovery of relations satisfied by the fluctuations in nonequilibrium steady states has become a major area of activity in the last decade. The ...
... gives a simple argument to show that the transport coefficients must be non-negative. The discovery of relations satisfied by the fluctuations in nonequilibrium steady states has become a major area of activity in the last decade. The ...
Contents
6 | |
11 | |
The microscopic connection | 33 |
The Greenkubo relations | 79 |
Linearresponse theory | 95 |
Computer simulation algorithms | 119 |
Nonlinear response theory | 167 |
Dynamical stability | 209 |
Nonequilibrium fluctuations | 259 |
Thermodynamics of steady states | 283 |
References | 301 |
Index | 309 |
Common terms and phrases
¼ ð ¼À ÀÁ adiabatic algorithm attractor autocorrelation function boundary conditions calculate canonical ensemble conjugate consider constant constitutive relation constraint correlation function defined definition density derivative difficulty dimension dissipative eigenvalues entropy equations of motion ergodic Evans and Morriss evolution exponential expression external field Figure finite first fixed fluctuation theorem fluid flux force Gauss Gaussian isokinetic gives Green–Kubo relations Hamiltonian infinite initial integral internal energy Jarzynski equality Kawasaki kinetic energy Langevin equation Lennard–Jones linear response theory Liouville equation Liouvillean Lyapunov exponents microscopic molecular dynamics momenta momentum Navier–Stokes NEMD nonequilibrium steady nonequilibrium systems nonlinear response obtained operator particle perturbation phase point phase space phase variable planar Couette flow pressure tensor propagator Section shear rate shear stress shear viscosity SLLOD equations steady-state streaming velocity sufficiently tensor thermal thermodynamic temperature thermostat time-dependent trajectory transport coefficients TTCF unstable manifolds vector XN i¼1 zero
Popular passages
Page i - Engineers, a Fellow of the Institute of Physics, and a Member of the Institute of Welding.
Page 243 - Since the determinant of a product is equal to the product of the determinants, Eq.
Page 268 - ... the rate at which work is done on the system by the applied loads.
Page 284 - ... sulfate, both rods come to electrical equilibrium with the solution. If they are connected by a wire, however, it is found that they are not in electrical equilibrium with each other, as evidenced by an electric current in the wire. The experimental results above can be stated...
Page i - D., has been a lecturer in the School of Physics at the University of New South Wales, Australia, since 1990.
Page 30 - Linear irreversible thermodynamics that Maxwell believed that all fluids are viscoelastic. The reason why polymer melts are observed to exhibit viscoelasticity is that their Maxwell relaxation times are macroscopic, of the order of seconds. On the other hand, the Maxwell relaxation time for argon at its triple point is approximately 10~12 seconds! Using standard viscometric techniques elastic effects are completely unobservable in argon.
Page 1 - Mechanics provides a complete microscopic description of the state of a system. When the equations of motion are combined with initial conditions and boundary conditions, the subsequent time evolution of a classical system can be predicted. In systems with more than just a few degrees of freedom such an exercise is impossible.
Page 1 - ... for such systems. Thermodynamics provides a theoretical framework for correlating the equilibrium properties of such systems. If the system is not at equilibrium, fluid mechanics is capable of predicting the macroscopic nonequilibrium behaviour of the system.
Page 32 - Equations (2.56b), are only observable if the strain rate varies significantly over either the time or length scales characteristic of the molecular relaxation for the fluid. The surprise is not so much that the validity of the Newtonian constitutive relation is limited. The more remarkable thing is...