Information‐theoretical analysis of a classical relativistic gas under a steady heat flow

The aim of this paper is to provide a simple illustration of how the thermodynamic analysis of equilibrium states may be generalized to nonequilibrium steady states characterized by a nonvanishing heat flow. To achieve this aim, we use maximum‐entropy arguments to describe a relativistic ideal gas under the constraints on the mean values of the internal energy and the heat flow. The partition function, the entropy, and the pressure tensor are obtained in terms of the internal energy, volume, number of particles, and heat flow. In the limit of vanishing heat flow, we recover the usual equilibrium thermodynamics. Thus our analysis exhibits in an explicit way some of the most relevant modifications of the thermodynamic quantities in presence of the heat flow.