Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

It has been shown in an earlier work [arXiv: 1303.1535] that there exists a pair of canonically conjugate variables (f(ab), N-bc(a)) in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations (f(bc)delta N-bc(a), N-bc(a)delta f(bc)), which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with (S delta T, T delta S) where (T, S) are the temperature and entropy. We generalize these results to Lanczos-Lovelock models in this paper. We identify two such variables in Lanczos-Lovelock models such that (a) our results reduce to that of general relativity in the appropriate limit and (b) the variation of the surface term in the action, when evaluated on a null surface, has direct thermodynamic interpretation as in the case of general relativity. The variations again correspond to S delta T and T delta S where S is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.