Kinetic temperatures and inertial effects in a nonequilibrium bead-spring model

Abstract

We investigate a nonequilibrium steady-state model consisting of two coupled beads with arbitrary masses in contact with two thermal baths at different temperatures. Using a covariance-matrix approach together with numerical simulations of the underdamped Langevin dynamics, we characterize steady-state probability distributions, heat transport, and entropy production. We show that irreversibility measures such as entropy production and heat current are invariant under an exchange of the bead masses, whereas energy-storage observables depend explicitly on the mass arrangement in a symmetrical set up. This reveals a fundamental distinction: energy observables exhibit path dependence in singular mass limits, while transport and irreversibility remain well defined. We show that kinetic temperatures provide the natural variables governing the thermodynamics of the system: their difference controls transport and entropy production, while their sum determines the mean energy via a model specific generalized equipartition relation. In the infinite-mass limit, only constitutive relations expressed in terms of kinetic temperatures remain meaningful. Thus, energy, transport, and irreversibility are unified through kinetic temperatures as the organizing variables. We also derive an effective temperature that defines an equilibrium-like canonical distribution. Finally, we analyze the notion of ergodicity and show that the time-averaged observables converge significantly faster than the ensemble averages.