The Boltzmann factor through experiments and simulations

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Abstract

The Boltzmann factor is at the basis of a great amount of thermodynamic and statistical physics,both classical and quantum. It describes the behaviour of natural systems that are exchangingenergy with the environment. However, why does the expression have this specific form? TheFeynman Lectures on Physics justifies it heuristically by reference to the “exponentialatmosphere” example. Thermodynamics textbooks usually give a more or less completeexplanation that mainly involves the mathematical analysis, where it is hard to see the logicflow. Moreover, the necessary mathematics is not at the level of high school or college students’preparation. Here we present an experiments and a simulation designed in order to directlyderive the Boltzmann factor expression and to illustrate the fundamental concepts and principlesof statistical mechanics. Experiments and simulations are used in order to visualise themechanisms involved; the first use easily available laboratory equipment, and simulations aredeveloped in NetLogo, a software environment that, besides having a really friend interface,allows the user to easily interact with the algorithm, as well as to modify it.
Lingua originaleEnglish
Numero di pagine0
Stato di pubblicazionePublished - 2009

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N2 - The Boltzmann factor is at the basis of a great amount of thermodynamic and statistical physics,both classical and quantum. It describes the behaviour of natural systems that are exchangingenergy with the environment. However, why does the expression have this specific form? TheFeynman Lectures on Physics justifies it heuristically by reference to the “exponentialatmosphere” example. Thermodynamics textbooks usually give a more or less completeexplanation that mainly involves the mathematical analysis, where it is hard to see the logicflow. Moreover, the necessary mathematics is not at the level of high school or college students’preparation. Here we present an experiments and a simulation designed in order to directlyderive the Boltzmann factor expression and to illustrate the fundamental concepts and principlesof statistical mechanics. Experiments and simulations are used in order to visualise themechanisms involved; the first use easily available laboratory equipment, and simulations aredeveloped in NetLogo, a software environment that, besides having a really friend interface,allows the user to easily interact with the algorithm, as well as to modify it.

AB - The Boltzmann factor is at the basis of a great amount of thermodynamic and statistical physics,both classical and quantum. It describes the behaviour of natural systems that are exchangingenergy with the environment. However, why does the expression have this specific form? TheFeynman Lectures on Physics justifies it heuristically by reference to the “exponentialatmosphere” example. Thermodynamics textbooks usually give a more or less completeexplanation that mainly involves the mathematical analysis, where it is hard to see the logicflow. Moreover, the necessary mathematics is not at the level of high school or college students’preparation. Here we present an experiments and a simulation designed in order to directlyderive the Boltzmann factor expression and to illustrate the fundamental concepts and principlesof statistical mechanics. Experiments and simulations are used in order to visualise themechanisms involved; the first use easily available laboratory equipment, and simulations aredeveloped in NetLogo, a software environment that, besides having a really friend interface,allows the user to easily interact with the algorithm, as well as to modify it.

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