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By Phil Attard

`Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications' builds from easy ideas to complex innovations, and covers the key phenomena, tools, and result of time-dependent structures. it's a pedagogic advent, a finished reference handbook, and an unique study monograph. Uniquely, the booklet treats time-dependent structures by way of shut analogy with their static opposite numbers, with lots of the normal result of equilibrium thermodynamics and statistical mechanics being generalized and utilized to the non-equilibrium case. The booklet is remarkable for its unified remedy of thermodynamics, hydrodynamics, stochastic tactics, and statistical mechanics, for its self-contained, coherent derivation of various non-equilibrium theorems, and for its quantitative assessments opposed to experimental measurements and laptop simulations.

Systems that evolve in time are extra universal than static structures, and but until eventually lately they lacked any over-arching concept. 'Non-equilibrium Thermodynamics and Statistical Mechanics' is exclusive in its unified presentation of the speculation of non-equilibrium structures, which has now reached the level of quantitative experimental and computational verification. the radical standpoint and deep figuring out that this e-book brings deals the chance for brand new course and development within the learn of time-dependent phenomena.

'Non-equilibrium Thermodynamics and Statistical Mechanics' is a useful reference handbook for specialists already operating within the box. learn scientists from diverse disciplines will locate the assessment of time-dependent structures stimulating and thought-provoking. academics in physics and chemistry should be thinking about many clean principles and themes, insightful factors, and new methods. Graduate scholars will take advantage of its lucid reasoning and its coherent process, in addition to from of mathematical concepts, derivations, and laptop algorithms.

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7. 6 Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. 6. 1 remoted procedure . . . . . . . . . . . . . . . . . . . . . 7. 6. 2 Canonical Equilibrium approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred forty five 146 146 147 148 one hundred fifty 154 154 154 157 157 157 159 161 163 173 174 176 176 177 177 one hundred eighty 182 184 186 186 186 188 192 194 195 195 198 203 205 207 210 210 214 216 218 219 220 xiv specific Contents 7. 7 Trajectory chance and Time Correlation features 7. 7. 1 Trajectory likelihood . . . . . . . . . . . . . . . 7. 7. 2 Equilibrium Averages . . . . . . . . . . . . . . . 7. 7. three Time Correlation services . . . . . . . . . . . . 7. 7. four Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 226 227 227 229 eight Non-Equilibrium Statistical Mechanics eight. 1 normal concerns . . . . . . . . . . . . . . . . . . . . . eight. 2 Reservoir Entropy . . . . . . . . . . . . . . . . . . . . . . . eight. 2. 1 Trajectory Entropy . . . . . . . . . . . . . . . . . . . eight. 2. 2 aid to the purpose Entropy . . . . . . . . . . . . eight. 2. three Fluctuation shape for the Reservoir Entropy . . . . . eight. three Transitions and movement in section house . . . . . . . . . . . eight. three. 1 Foundations for Time established Weight . . . . . . eight. three. 2 Fluctuation kind of the second one Entropy . . . . . . . eight. three. three Time Correlation functionality . . . . . . . . . . . . . . eight. three. four Stochastic, Dissipative Equations of movement . . . . . eight. three. five Transition likelihood and Fokker-Planck Equation . eight. three. 6 probably strength with Constraints . . . . . . . . . . eight. four adjustments in Entropy and Time Derivatives . . . . . . . . . . eight. four. 1 swap in Entropy . . . . . . . . . . . . . . . . . . . eight. four. 2 Irreversibility and Dissipation . . . . . . . . . . . . . eight. four. three a number of Time Derivatives . . . . . . . . . . . . . . . eight. four. four regular nation process . . . . . . . . . . . . . . . . . . eight. five extraordinary Projection of the Dynamic Reservoir Entropy . . . . . eight. 6 direction Entropy and Transitions . . . . . . . . . . . . . . . . . eight. 6. 1 course Entropy . . . . . . . . . . . . . . . . . . . . . . eight. 6. 2 Fluctuation and paintings Theorem . . . . . . . . . . . . eight. 7 direction Entropy for Mechanical paintings . . . . . . . . . . . . . . eight. 7. 1 Evolution of the Reservoir Entropy and Transitions . eight. 7. 2 Transition Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 233 235 235 237 239 240 240 244 247 249 258 260 262 262 266 268 273 275 280 280 287 289 289 292 nine Statistical Mechanics of regular move: warmth and Shear nine. 1 Thermodynamics of regular warmth circulation . . . . . . . . . . nine. 1. 1 Canonical Equilibrium method . . . . . . . . . . nine. 1. 2 Fourier’s legislations of warmth Conduction . . . . . . . . nine. 1. three moment Entropy for warmth stream . . . . . . . . . . nine. 2 section house likelihood Density . . . . . . . . . . . . . nine. 2. 1 particular Hamiltonian and primary strength second . nine. 2. 2 Reservoir Entropy and chance Density . . . nine. three probably Trajectory . . . . . . . . . . . . . . . . . . . nine. four Equipartition Theorem for warmth movement . . . . . . . . . . nine. five Green-Kubo Expressions for the Thermal Conductivity . nine. five. 1 remoted process . . . . . . . . . . . . . . . . . . . nine. five. 2 warmth Reservoirs . . . . . . . . . . . . . . . . . . . nine. five. three Relation with bizarre Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 295 295 296 299 303 303 306 308 310 313 313 315 318 . . . . . . . . . . . . . . . . . . . . . . . . . . designated Contents nine. 6 Shear nine. 6. 1 nine. 6. 2 nine. 6. three nine. 6. four stream . . . . . .

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