Generalised complex geometry in thermodynamical fluctuation theory

We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction. Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM. (2015). Generalised complex geometry in thermodynamical fluctuation theory. Entropy. 17(8):5888-5902. doi:10.3390/e17085888 Velazquez Abad, L. (2012). Principles of classical statistical mechanics: A perspective from the notion of complementarity. Annals of Physics, 327(6), 1682-1693. doi:10.1016/j.aop.2012.03.002 Bravetti, A., & Lopez-Monsalvo, C. S. (2015). Para-Sasakian geometry in thermodynamic fluctuation theory. Journal of Physics A: Mathematical and Theoretical, 48(12), 125206. doi:10.1088/1751-8113/48/12/125206 Bravetti, A., Lopez-Monsalvo, C. S., & Nettel, F. (2015). Contact symmetries and Hamiltonian thermodynamics. Annals of Physics, 361, 377-400. doi:10.1016/j.aop.2015.07.010 Quevedo, H., Vázquez, A., Macias, A., Lämmerzahl, C., & Camacho, A. (2008). The geometry of thermodynamics. AIP Conference Proceedings. doi:10.1063/1.2902782 Rajeev, S. G. (2008). Quantization of contact manifolds and thermodynamics. Annals of Physics, 323(3), 768-782. doi:10.1016/j.aop.2007.05.001 Rajeev, S. G. (2008). A Hamilton–Jacobi formalism for thermodynamics. Annals of Physics, 323(9), 2265-2285. doi:10.1016/j.aop.2007.12.007 Ruppeiner, G. (1995). Riemannian geometry in thermodynamic fluctuation theory. Reviews of Modern Physics, 67(3), 605-659. doi:10.1103/revmodphys.67.605 Velazquez, L. (2013). Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory. Journal of Physics A: Mathematical and Theoretical, 46(34), 345003. doi:10.1088/1751-8113/46/34/345003 Bardeen, J. M., Carter, B., & Hawking, S. W. (1973). The four laws of black hole mechanics. Communications in Mathematical Physics, 31(2), 161-170. doi:10.1007/bf01645742 Padmanabhan, T. (2010). Thermodynamical aspects of gravity: new insights. Reports on Progress in Physics, 73(4), 046901. doi:10.1088/0034-4885/73/4/046901 Padmanabhan, T. (2014). General relativity from a thermodynamic perspective. General Relativity and