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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 $(f^{ab},N^a_{bc})$ in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations $(f^{bc}δN^a_{bc}, N^a_{bc}δf^{bc})$, which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with $(SδT,TδS)$ 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 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 $SδT$ and $TδS$ where $S$ is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.