Can Quantum Thermodynamics Save Time?

The thermal time hypothesis (TTH) is a proposed solution to the problem of time: every statistical state determines a thermal dynamics according to which it is in equilibrium, and this dynamics is identified as the flow of physical time in generally covariant quantum theories. This paper raises a series of objections to the TTH as developed by Connes and Rovelli (1994). Two technical challenges concern the implementation of the TTH in the classical limit and the relationship between thermal time and proper time. Two more conceptual problems focus on interpreting the flow of time in non-equilibrium states and the lack of gauge invariance