Oosawa’s Preface

This book is intended to be an introduction to statistical mechanics.Although there are many introductory books and references on this subject, the policy of this book is different from that of other related works in that importance is placed on empirical examples and intuitive argument.It is the author's hope that, through the use of this book, all readers will be able to learn statistical mechanics with a clear imagination of molecular behavior, allowing them to "enter the gate 0.1 ", so to speak.When making arguments in statistical mechanics, we often imagine that numerous particles gather, with each capable of free motion.In comparison, in this book, we begin by considering just a small number of particles.We then attempt to describe the movement of each individual particle, as well as the collective movement of these (small number of) particles as a whole.For that purpose, we make frequent use of the behavior of "dice" to represent the individual movement of particles and "gaming chips" to represent the energy of these particles.According to the rules of the game these chips are able to be exchanged and grouped according to the numbers on the dice.Through observation of how the gaming chips are distributed upon rolling the dice under various settings, many unexpected situations can occur, some of which may surprise even "professional" researchers.The essence of statistical mechanics exists in this unpredictability, and I would like you to carefully observe these outcomes while rolling the dice yourself."DIY statistical mechanics" can be established as a result.The basic concepts of statistical mechanics, such as entropy, free energy, and temperature, can be quite simply developed from the dice and gaming chips approach.By examining both the movement of each particle in the group, their collective average movement as a whole, and the rate of change of those average quantities, you will be able to understand these fundamental concepts (entropy, free energy and temperature) intuitively.I recommend that after solving these simple problems (either by playing the described games or making diagrams) that you then compare the approach used here to that adopted in other textbooks on statistical mechanics.It is my belief that the topic of statistical mechanics can be best understood based on the accurate determination of the mechanical behavior of small numbers of particles.Using this approach, interesting viewpoints on difficult (yet important) problems at the front line of biological and physical research, such as the "temperature" of single macromolecules, will naturally emerge.Using such concepts as "local temperature", one can infer general aspects about the three-dimensional structure of individual macromolecules (tiny rods and bars), such as their general shape and flexibility.It would be gratifying, if the methods described in this book allow you, the reader, to develop a clearer understanding of some of these difficult concepts in current biological and physical research.The general approaches described herein extend to subjects that appear to have no direct relation to "statistical mechanics".Such deeper understanding can lead the reader to the great discovery that Brownian motion and harmonic functions in potential theory are directly related.Furthermore, the qualitative differences between one-dimensional, two-dimensional, and three-dimensional Brownian motion, can be understood mathematically, and can also be "realized" from the game involving the rolling of dice.In summary, using the dice and gaming chips approach, I want you to convince yourself that the presented ideas are correct.This book presents several exceedingly difficult problems, with Feynman's ratchet being one of these.Even if you do

Abstract licence: CC BY-NC-SA

1 more reference, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.