A word on the better methods Jaynes refers to: these are [1] and [2] in the References. I actually encountered [2], Truesdell’s Rational Thermodynamics, previously as a consequence of this community.
The pitch here is basically tackling thermodynamics from axioms with field equations. In particular Truesdell advocated a method of moments, which is to say keep adding fields of the behavior you are concerned with to refine the answer.
Truesdell was important to the field of Continuum Mechanics, which is still used in engineering. The idea here is that rather than calculating what happens to each particle of a material, the material is treated as a continuum, and then you calculate the change in the particular property you are concerned with. This is an efficient way to get numerical answers about stress, shear, heat conduction, memory effects, tearing, etc. Rational Thermodynamics is generalizing the continuum method. They have proved Navier-Stokes as a special case of the method of moments, although they also demonstrated that many additional moments does not significantly outperform Navier-Stokes. The suggestion is that it may take hundreds or thousands of moments to get an improvement here, which was impractical at the time Truesdell was writing. However, that was before we had really powerful computing tools for addressing problems like this.
The way I got to Truesdell was through an anonymous blog from a poster on either the old LessWrong or possibly even the joint Overcoming Bias posts, and in that blog they referenced a review Jaynes did of one of Truesdell’s papers. Jaynes was impressed that Truesdell had arrived at virtually the same formalism that Jaynes himself had, through purely mathematical means.
This is not important, except for being cool and motivating me to look into Rational Thermodynamics.
A word on the better methods Jaynes refers to: these are [1] and [2] in the References. I actually encountered [2], Truesdell’s Rational Thermodynamics, previously as a consequence of this community.
The pitch here is basically tackling thermodynamics from axioms with field equations. In particular Truesdell advocated a method of moments, which is to say keep adding fields of the behavior you are concerned with to refine the answer.
Truesdell was important to the field of Continuum Mechanics, which is still used in engineering. The idea here is that rather than calculating what happens to each particle of a material, the material is treated as a continuum, and then you calculate the change in the particular property you are concerned with. This is an efficient way to get numerical answers about stress, shear, heat conduction, memory effects, tearing, etc. Rational Thermodynamics is generalizing the continuum method. They have proved Navier-Stokes as a special case of the method of moments, although they also demonstrated that many additional moments does not significantly outperform Navier-Stokes. The suggestion is that it may take hundreds or thousands of moments to get an improvement here, which was impractical at the time Truesdell was writing. However, that was before we had really powerful computing tools for addressing problems like this.
The way I got to Truesdell was through an anonymous blog from a poster on either the old LessWrong or possibly even the joint Overcoming Bias posts, and in that blog they referenced a review Jaynes did of one of Truesdell’s papers. Jaynes was impressed that Truesdell had arrived at virtually the same formalism that Jaynes himself had, through purely mathematical means.
This is not important, except for being cool and motivating me to look into Rational Thermodynamics.