Review of Newtonian Mechanics, Basic Statistical Mechanics, and Hessians

2020 ◽  
pp. 217-219
Author(s):  
W. John Dartnall ◽  
John Reizes ◽  
Geoff Anstis

The laws of thermodynamics provide an adequate basis for the development of classical thermodynamics and for the many empirical relationships used by mechanical and chemical engineers. The laws evolved before the advent of the computer with its ability to handle complex simulations. This led to the classical structure that did not require a molecular view of matter. The concept of entropy grew out of this classical view but, has unfortunately earned a reputation for being something mysterious and difficult. Statistical mechanics, much of which is based on Newtonian mechanics, has the power to remove the mystery. But, because of its mathematical complexity, it has rarely been used by engineers either to clarify understanding or to analyze processes and models. We propose, illustrating with examples, that simple Newtonian mechanical models can be used in place of statistical mechanics — at least for the teaching of concepts. Surprisingly, the models developed using Newton’s three Laws allow the development of the zeroth, first and second laws of thermodynamics and the processes by which equilibrium is reached. We believe that in teaching thermodynamics the links with Newtonian mechanics would best be established by the proposed simple methods because of the resulting enlivening of Newtonian mechanics and the enhanced understanding of the fundamental concepts of thermodynamics.


Author(s):  
W. John Dartnall ◽  
John A. Reizes

As a subject in an engineering course, Engineering Thermodynamics has earned a reputation for being difficult to understand. Quite often students practice many problems until they can do the assigned tasks, but they still feel mystified by concepts such as entropy. Even though we may use them competently, energy, enthalpy and temperature are not necessarily well understood at a concept level. Statistical Mechanics provides an excellent way of understanding the concepts more fundamentally but the traditional mathematical derivations in Statistical Mechanics require considerable time and effort before a learner gains the comfort of familiarity. Various approaches using spread-sheets to construct combinatorial illustrative examples have been published. An approach based on molecular dynamic simulation is presented in this paper, in which comparisons between actual outcomes of simulations based solely on Newtonian mechanics are compared with the probability based models. Accordingly, this approach allows explanations which meet the objective of demystifying some of the concepts that have hitherto been the bane of undergraduate thermodynamics.


2020 ◽  
Author(s):  
Douglas Michael Snyder

The mind of man is central to the structure and functioning of the physical world. Modern physical theory indicates that the mind stands in a relationship of equals to the physical world. Both are fundamental, neither can be reduced to the other, and both require each other for their full understanding. This thesis is at odds with the view of the universe found in Newtonian mechanics as well as the generally held view among contemporary physicists of modern physical theory. Since the Renaissance, people have come to understand a great deal about the physical world, and they have gained significant control over it. This increased power over the physical world has occurred hand in hand with the assumption that the structure and functioning of the physical world is essentially independent from human cognition. According to this assumption, if a person’s cognitive capacity did not exist, the functioning of the physical world would not be fundamentally altered. This last statement is not in fact correct, and modern physical theory, and even fundamentals underlying Newtonian mechanics, provide evidence to attest to this. Nonetheless, contemporary physicists for the most part do not see that the relationship of human cognition to the physical world is radically altered in their own modern theory, theory that is supported by a great deal of empirical data. Instead, attempting to preserve the thesis that the structure and functioning of the physical world is independent of the mind while on a practical level relying on modern theory that contradicts this thesis, physicists have placed themselves in the position of wondering at times exactly what is the nature of the physical world at the same time they obtain experimental results concerning the physical world that can only be labeled astonishing in their precision and the scope of their implications. Modern physical theory consists of three main components: 1) the special and general theories of relativity; 2) quantum mechanics; and 3) statistical mechanics. There are very successful theories that have been developed on the basis of these three bedrock areas. An example is quantum electrodynamics. But these theories owe their conceptual foundation to the three components mentioned. The basic issues at the core of these three components also are expressed in these later theories. In addition, there are new unresolved issues of a fundamental nature concerning the conceptual integrity of these later theories that do not apply to quantum mechanics, relativity theory, and statistical mechanics. Quantum mechanics and relativity theory are areas I have written about for over twelve years. The nature of statistical mechanics has also been of interest to me during this time. But when I took a serious look in 1993 at Tolman’s (1938) The Principles of Statistical Mechanics, it became clear that the mind is linked to the physical world in statistical mechanics, a relationship I had found earlier in both relativity theory and quantum mechanics. It was after reading Tolman’s justification of the method of statistical mechanics in the original that I decided to write this book. When I found that the three components of modern physical theory all pointed to the same relationship between mind and the physical world, it became clear that the fundamental isolation of the mind from the physical world that has characterized our experience since the development of Newtonian mechanics is unfounded. Based on empirically supported principles of modern physical theory, I determined that the appropriate assumption for one’s experience, that the mind is linked to the physical world, could be stated with confidence. The impact of this change in assumption concerning the relationship of man to the cosmos in modern physical theory will find its way into our everyday experience. It will perhaps have no greater effect than in reducing the sense of isolation of man from the world that has characterized modern existence.


1992 ◽  
Vol 2 (5) ◽  
pp. 1215-1236 ◽  
Author(s):  
Jonathan V. Selinger ◽  
Robijn F. Bruinsma

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