# Second Law of Thermodynamics in Terms of Electromagnetic Principles?

In Heaviside's Electromagnetic Theory (1895) he says that "The second law of thermodynamics itself needs to be established from electromagnetic principles, assisted by the law of averages..."

I attempted to Google whether or not anyone has derived the second law via electricity and magnetism, but couldn't find anything. I'm guessing this has been accomplished so can anyone point me in the right direction?

You should look at the statistical mechanics interpretration of Entropy, and how that leads to the second law of Thermodynamics. Essentially, if you have charged particles, you can incorporate the electromagnetic terms into the Hamiltonian of the system, calculate the partition function, and work out and expression for the Entropy.

1 person
Jano L.
Gold Member
In Heaviside's Electromagnetic Theory (1895) he says that "The second law of thermodynamics itself needs to be established from electromagnetic principles, assisted by the law of averages..."

I attempted to Google whether or not anyone has derived the second law via electricity and magnetism, but couldn't find anything. I'm guessing this has been accomplished so can anyone point me in the right direction?
In thermodynamics, the second law is an empirical law and this allows us to use it to derive other, less obvious laws. In thermodynamics, it does not "need" to be established from other principles, electromagnetic or other.

But still it would be interesting to see some version of it to be derived from another law, preferably just as acceptable as a basic assumption. This could be of great help in bringing different ares of physics together and in providing new views on the old knowledge.

In statistical physics, people invented convincing arguments based on probability considerations that show the second law is valid with probability very close to 1 for systems of classical mechanics with many particles. These systems are not representative of electromagnetic theory though - they do not take into account Maxwell's equations or finite propagation of interaction.

I believe potential merger of electromagnetic theory with statistical physics still needs a lot of thinking. Heaviside's goal has not been reached yet.