Position dependent mass dissipative scalar field at finite temperature

Position dependent mass dissipative scalar field is a theoretical framework that combines the concepts of position-dependent mass and dissipative systems in the context of scalar field theory. In this framework, the mass of the scalar field is allowed to vary with position, leading to interesting physical phenomena such as non-locality and non-Hermiticity. We consider a generalized classical Lagrangian for the system and by developing a theoretical formulation, quantized system canonically. In follow, two-point correlation functions of the system is obtained at finite temperature and Free energy of the system is calculated in terms of Matsubara frequencies. This research can provide insights into the behavior of particles and fields in non-uniform environments, and has potential applications in various fields of physics.