The surface plasmon excitation spectrum is calculated for the Weyl semimetal within the random phase approximation. Recently, a surface plasmon mode has been predicted to exist at the three-dimensional Dirac semimetal surface due to the Dirac plasmon mode in the bulk. In addition, Weyl semimetals possess Fermi arc electron states on their surfaces resulting in an anisotropic Fermi arc plasmon mode. In the present work we consider the modification of the surface plasmon mode due to the Fermi arc plasmon mode. We introduce an effective surface dielectric function of Fermi arc electrons which comprises the Fermi arc plasmon mode and the surface dielectric function that determines the bare surface plasmon mode present due to the plasmon mode in the bulk from Weyl electrons. As a result, we obtain the dispersion of the renormalized surface plasmon mode from the effective surface dielectric function. We find that a renormalization of the bare surface plasmon mode increases with increases in the Fermi arc plasmon frequency. The obtained spectrum will be useful for experimentally exploring the surface spectral properties of Weyl semimetals.

It is shown that Onsager’s principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of stationary processes, that this extremum is a maximum rather than a minimum.

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.