Abstract
In 1867, just two years after laying the foundations of electromagnetism, J. Clerk Maxwell presented a fundamental paper on kinetic gas theory, in which he described the evolution of the gas in terms of certain ‘moments’ of its velocity distribution function. This inspired Ludwig Boltzmann to formulate his famous kinetic equation, from which followed the H-theorem and the connection with entropy. On the occasion of the 150th anniversary of publication of Maxwell's paper, we review the Maxwell–Boltzmann formalism and discuss how its generality and adaptability enable it to play a key role in describing the behaviour of a variety of systems of current interest, in both gaseous and condensed matter, and in modern-day physics and technologies which Maxwell and Boltzmann could not possibly have foreseen. In particular, we illustrate the relevance and applicability of Maxwell's formalism to the dynamic field of plasma-wakefield acceleration.
Highlights
Clerk Maxwell is regarded as one of the most influential physicists of all time [1,2,3], and his work continues to underpin many areas of modern-day scientific research and technological development. He is best known for his equations of electromagnetism [4], but is recognised for seminal contributions in other areas of physics, including statistical mechanics and kinetic theory
The most significant contribution to the field came in a paper presented to the Royal Society of London 150 years ago [6], in which he linked the microscopic world of atoms with macroscopically measurable properties, through velocity averages or ‘moments’ of a nonequilibrium velocity distribution function f (r, v, t)
Its applicability ranges from traditional gas transport theory to present-day cutting-edge research on ultra-relativistic electron beams in plasma-wakefield accelerators
Summary
Clerk Maxwell (pictured in figure 1) is regarded as one of the most influential physicists of all time [1,2,3], and his work continues to underpin many areas of modern-day scientific research and technological development He is best known for his equations of electromagnetism [4], but is recognised for seminal contributions in other areas of physics, including statistical mechanics and kinetic theory. The most significant contribution to the field came in a paper presented to the Royal Society of London 150 years ago [6], in which he linked the microscopic world of atoms with macroscopically measurable properties, through velocity averages or ‘moments’ of a nonequilibrium velocity distribution function f (r, v, t) In this paper, he developed ‘moment equations’, sometimes referred to as ‘equations of change’, describing the evolution of the properties of a mixture of two monatomic gases, accounting explicitly for the influence of collisions between atoms. It is only in the equilibrium limit that Maxwell discusses an explicit form of the distribution function
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