Landau & Lifschitz's fluid mechanics book proposes the following statement for an isentropic proccess: $$dH=vdp \Rightarrow \nabla H=v\nabla p$$ What's the rigorous way to get this result (converting differentials to gradients)? Thanks in advance.

when I rub together the quartz, it glows due to triboluminescence but it also creates a burnt smell. I want to know what causes that smell?

I found something that I'm confused with when calculating the propagator of harmonic oscillator. Using the energy representation, the propagator of a quantum harmonic oscillator can be expressed as : $$ K(x_f,t_f;x_i,t_i)=\sum_ne^{-i\omega T(n+\frac{1}{2})}\psi_n(x_f)\psi_n^*(x_i)\tag{1} $$ where...

My understanding of fermions, bosons, and anyons is that anyons are disallowed in 3+1 dimensions (or $n+1 | n\geq3$) because of the topology of spacetime. The paths of swapping two particles twice is contractible in 3+1. In 2+1, this isn't the case and so anyons can exist. However, what is the ca...