It is usually taken for granted that the scheme we use to characterize distances will have no effect on our measurement. More formally, physical systems are invariant under coordinate transformations. As a result, the energy-momentum tensor is conserved. In a seminal paper, Alvarez-Gaume and Witten have shown that coordinate transformations can become anomalous: due to quantum effects invariance under coordinate transformations is broken and the energy-momentum tensor is no longer conserved. This breaking of coordinate invariance is called a gravitational anomaly.
In a recent publication, A. Yarom together with K. Jensen from the University of Victoria and R. Loganayagam from Harvard studied the impact of gravitational anomalies on thermodynamic behavior. Quite surprisingly, these anomalies affect the thermodynamic behavior of the system in a strikingly pronounced way than has been anticipated; the response of the equilibrated system to particular perturbations is controlled by the strength of gravitational anomalies. Gravitational anomalies, one of the most subtle effects of quantum mechanics, may play an important role in characterizing thermodynamic equilibria of various physical systems.