Analysis of temperature gradient effects on thermodynamic properties of relativistic scalar field model

Recent experimental and theoretical investigations have revealed that relativistic heavy ion collisions lead to the formation of a quark-gluon plasma (QGP), which behaves as an almost perfect fluid described by relativistic hydrodynamic models . The hydrodynamic equations used in these models have been conventionally relied on a derivative expansion, assuming that spatial derivatives of local thermodynamic quantities (e.g., temperature) are sufficiently small.

However, it is important to note that temperature gradients within the produced QGP can reach magnitudes of 100 MeV/fm, which is not small. Consequently, it remains uncertain whether the conventional hydrodynamic equation, based on the derivative expansion, can be reliably applied to the QGP. In this presentation, we will explore the effects arising from a potentially large temperature gradient by incorporating it to finite-temperature quantum field theory. Specifically, we will apply the imaginary-time formalism for local thermal equilibrium to the relativistic scalar field model to examine how temperature gradients influence thermodynamic properties such as the partition function and pressures.