Covariant Thermodynamics of Quantum Systems: Passivity, Semipassivity, and the Unruh Effect

According to the Second Law of Thermodynamics, cycles applied to thermodynamic equilibrium states cannot perform any work (passivity property of thermodynamic equilibrium states). In the presence of matter this can hold only in the rest frame of the matter, as moving matter makes windmills and turbines run. If, however, one assumes for a homogeneous and stationary state that no cycle can perform more work than an ideal windmill, one finds that there is some inertial frame where the state is a thermodynamic equilibrium state. This provides a covariant characterization of thermodynamic equilibrium states.In the absence of matter, cycles can perform work only when driven by nonstationary inertial forces. If this is taken as a definition of a (pure) vacuum state of a relativistic quantum field theory, one can derive the spectrum condition and the Unruh effect.