The impact of tensorial temperature on equilibrium thermodynamics

Abstract

Thermodynamic temperature is a scalar. However, the connection with the kinetic energy tensor in statistical mechanics leaves open the possibility to define a tensorial temperature. This concept has sometimes been used to simulate isothermal conditions in out-of-equilibrium systems. Here, we show, by studying a sessile water droplet, that a tensorial temperature leads to the wrong thermodynamics, or, in other words, the equilibrium isothermal ensemble generated using a tensorial temperature is not the canonical one, with interfacial free energies that can differ up to 40% from the correct ones.