Non-Equilibrium Thermodynamics and Statistical Mechanics
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Non-Equilibrium Thermodynamics and Statistical Mechanics

Non-Equilibrium Thermodynamics and Statistical Mechanics Foundations and Applications by Phil Attard | PDF Free Download.

Thermodynamics and Statistical Mechanics Contents

  • Prologue 
  • Fluctuation Theory 
  • Brownian Motion
  • Heat Conduction 
  • Second Entropy for Fluctuating Hydrodynamics 
  • Heat Convection and Non-Equilibrium Phase Transitions 
  • Equilibrium Statistical Mechanics 
  • Non-Equilibrium Statistical Mechanics 
  • Statistical Mechanics of Steady Flow: Heat and Shear 
  • Generalized Langevin Equation 
  • Non-Equilibrium Computer Simulation Algorithms
  • References
  • Index

Preface to Non-Equilibrium Thermodynamics and Statistical Mechanics

All Things Change in Time

Motion and change are the nature of the world. The scale of motion ranges from the orbit of galaxies and planets, to the winds, ocean currents, and river flows, and even to the sub-microscopic, with the ceaseless movement of atoms and molecules.

In the living world, there is the locomotion of animals, the movement of limbs and muscles, and the flows of blood, sap, and other vital fluids.

It is also human-made motion in the form of transport by planes, trains, and automobiles, the mechanical movement of motorized tools, and controlled flows such as those of electricity, heat, and fluids. There are as well other forms of change.

Birth, growth, and death is a familiar trajectory for any individual living organism. But these also describe the evolution of a species as a whole, as well as that of the universe, planets, ecosystems, and even social structures.

One can also include other physical phenomena that are the subject of more traditional scientific study such as the progress of chemical reactions, the development of heat and current fluxes, the formation of patterns by aerodynamic and hydrodynamic flows, the processes of self-assembly and physical organization, and the dynamic deformation and response of materials.

These, of course, occur in nature, industry, technology, and under controlled laboratory conditions.

The rˆole of chance in our world should not be underestimated. When things occur, their exact trajectory and their ultimate fate are not perfectly predictable.

In general, the complexity of systems, unknown initial conditions, and the influence of uncontrolled external forces all contribute a degree of randomness that leads to an uncertain future unconstrained by a strict fatalism.

Chance means that changes in time occur not with pure determinism but rather with statistical probability

Time Changes Everything

The point belabored above is that time-dependent phenomena are ubiquitous. The technical word for these is ‘non-equilibrium’.

It is a reflection of the chronological development of science that this, the most common class of systems, is described in the negative.

Initially, thermodynamics and statistical mechanics were developed for equilibrium systems, which do not change macroscopically with time. Thermodynamics is the science of macroscopic systems, and it provides universal laws and relationships that all equilibrium systems must obey.

Statistical mechanics enables the probabilistic description of equilibrium systems at the molecular level. It gives the mathematical basis for the empirical laws of thermodynamics and it provides quantitative values for measured thermodynamic parameters.

It is one of the great ironies of science that the word ‘dynamics’ in ‘thermodynamics’, and the word ‘mechanics’ in ‘statistical mechanics’, both imply motion, when in fact both disciplines have been strictly formulated for static or equilibrium systems.

Of course, as an approximation, they are often applied to time-dependent systems, either instantaneously or else over time intervals small enough that any change is negligible, or they can be combined with an empirical theory such as hydrodynamics.

But in terms of an exact treatment, thermodynamics and statistical mechanics are restricted to equilibrium systems. This raises the question: How do time change thermodynamics and statistical mechanics?

Non-Equilibrium Thermodynamics and Statistical Mechanics PDF

This book seeks to answer that disarmingly simple question. A coherent formulation of non-equilibrium thermodynamics is given.

The approach is based upon a particular form of entropy, and it has the advantage that almost all of the concepts of equilibrium thermodynamics carry over to the non-equilibrium field.

It also enables a consistent derivation of most of the known non-equilibrium theorems and results, which exhibits their inter-relationships and places them in the context of a bigger picture.

The non-equilibrium probability distribution is also developed, and this provides a basis for the field of non-equilibrium statistical mechanics.

Again, this enables a unified derivation of known and previously unknown theorems. Importantly, it also enables the development of computer simulation algorithms for non-equilibrium systems, which are used to test quantitatively the results and to illustrate them at the molecular level.

Because of the significance of time-dependent phenomena, there are many books and scientific papers concerned with the formulation of non-equilibrium thermodynamics and non-equilibrium statistical mechanics, and with their application to specific systems.

The selection of topics, underlying approach, and method of presentation vary enormously, although certain non-equilibrium theorems and results for which there is broad consensus commonly recur.

Other results lie at the cutting edge of current research, and for this detailed justification and explanation are required.

As mentioned above, this book proceeds from the very fundamental principles that determine the optimum non-equilibrium thermodynamic state, and also from the equations of motion and probability distributions appropriate for non-equilibrium statistical mechanics.

The strategy employed here is to set out the physical basis of the axioms, the close analogy between non-equilibrium and equilibrium principles, and, most importantly, the theorems and detailed results that follow as a consequence.

In general, an attempt is made to provide quantitative tests, experimental or computational, and detailed comparisons between different approaches, and alternative, independent derivations of the same result.

It is hoped that such concrete evidence and the consistency of the approach will give some confidence in the fundamental principles that the book is based upon.

In the present book, most of the traditional topics in the non-equilibrium field are covered, and some new ones besides.

What is perhaps unique here is that a single underlying approach suffices to derive and to describe all these results.

The fields of non-equilibrium thermodynamics and non-equilibrium statistical mechanics are here regarded as a continuum that ranges from the macroscopic to the sub-microscopic, with Brownian motion and stochastic processes lying in the boundary region where they merge.

In a sense, this book is one long argument for non-equilibrium thermodynamics and statistical mechanics. There are several reasons why the reader may find the present approach useful and may have confidence in the results.

First, is the simplicity of the concepts, examples, and equations. Stripping away all that is unnecessary removes the possibility of confusion masquerading as complexity, and displays the results in a clear and unambiguous light.

Second, is the physical basis of the approach. Thermodynamics and statistical mechanics are derived from and designed for the real world, and here is emphasized the physical basis and interpretation of all the terms that occur in each equation.

This removes the likelihood of inadvertent non-physical behavior due to artificial assumptions, it gives an intuitive feel to the equations and results, and it enables the common sense test to be readily applied. Third, is the coherence and self-consistency of the approach.

Those theorems and results in non-equilibrium thermodynamics and statistical mechanics that are widely accepted are all derived here from a single approach based on entropy.

This consilience gives some confidence in both the approach itself and the new results also generated by it. Fourth, the results of a number of computer simulations are given in the text, both to illustrate the procedures and to test quantitatively the results.

In addition, certain experimental measurements are used, again quantitatively, to test predictions of the theory. Such tests should prove convincing, both of the individual results and of the formulation as a whole.

The fields of thermodynamics and statistical mechanics have grown over the years. This book is part of that evolution; it is intended to be timely rather than timeless.

The principles for non-equilibrium thermodynamics and statistical mechanics set out herein consolidate the present state of knowledge and provide a basis for future growth and new applications.

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