1278 Words3 Pages

Justin Ivins

Professor Rowell

Math 220

5 April 2014

Statistical Mechanics

Statistical mechanics is a very broad subject with many other concepts under its umbrella. This topic has entire classes dedicated to it, with hundreds of theories and equations, so instead of unrealistically trying to master a whole course I instead sought to get a general understanding of the topic to the point that I could apply what I learned to future courses featuring statistical mechanics. However, to understand the topic I obviously had to go in depth into the main points of the field, and examine the contributions that pushed the field forward. After my initial research I found that the topic of statistical mechanics is like the label on a tool box with dozens
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Classical mechanics explores the movement of bodies because of other sources, and can determine future and past locations of molecules at any time if given the location and velocity of a molecule at any one time. Classical can be very accurate if given large enough objects and the speed of an object is not near the speed of light (Leland). While classical deals with objects on a human scale, quantum mechanics deals with objects on an atomic scale. Quantum mechanics throws away the idea that we can define where a molecule’s trajectory is heading, so we must instead take probabilities and average the changing position over time (Leland). All of this is just the basic workings of physical mechanics without statistical mechanics added in it yet. Statistical mechanics combines the principles of statistics with the laws of classical and quantum mechanics, particularly with thermodynamics (Leland). Statistics gets added in with the idea of statistical ensembles, which are probability distributions over all possible states of the system. In quantum mechanics, statistical mechanics introduces stat ensembles that use a large collection in the system and creates a probability distribution over all the possible systems (Jackson). In classical mechanics, statistical mechanics uses a probability distribution over phase points as the ensemble
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Statistical thermodynamics is a branch of physics that applies probability theory to the study of the thermodynamic behavior of a large number of particles (Laurendeau). Statistical mechanics provides a blueprint for relating the microscopic properties of singular atoms and molecules to the macroscopic overall properties of materials that can be observed physically (Laurendeau). This relationship explains thermodynamics. Statistical mechanics provides an atom-sized interpretation of macroscopic thermodynamic characteristics such as heat, entropy, and work. It enables the thermodynamic properties of the whole object to be related to the microscopic data of individual atoms or molecules (Laurendeau). This ability to make macroscopic calculations based on microscopic characteristics is the main benefit of statistical mechanics over classical thermodynamics. Josiah Willard Gibbs used these definitions to explain the laws of thermodynamics as consequences of the statistical properties of large ensembles of particles, and officially created the field of statistical mechanics. His book Elementary Principles in Statistical Mechanics is considered the foundation of the field, and for the first time documented how quantum-like laws could arise from the old classical mechanical system

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