We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous paper [ Phys. Rev. D 103, L121501 (2021), upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart’s first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, “temperature of gravity,” viscosities, entropy density, plus an equation describing the “diffusion” to Einstein gravity. These quantities, still missing in the usual thermodynamics of spacetime, are obtained with minimal assumptions. Furthermore, we examine certain exact solutions of scalar-tensor gravity to test the proposed formalism and gain some physical insight on the “approach to equilibrium” for this class of theories.

This paper presents a mathematical approach to model the effects of phenomena with random nature such as turbulence and fire-spotting into the existing wildfire simulators. The formulation proposes that the propagation of the fire-front is the sum of a drifting component (obtained from an existing wildfire simulator without turbulence and fire-spotting) and a random fluctuating component. The modelling of the random effects is embodied in a probability density function accounting for the fluctuations around the fire perimeter which is given by the drifting component. In past, this formulation has been applied to include these random effects into a wildfire simulator based on an Eulerian moving interface method, namely the Level Set Method (LSM), but in this paper the same formulation is adapted for a wildfire simulator based on a Lagrangian front tracking technique, namely the Discrete Event System Specification (DEVS). The main highlight of the present study is the comparison of the performance of a Lagrangian and an Eulerian moving interface method when applied to wild-land fire propagation. Simple idealised numerical experiments are used to investigate the potential applicability of the proposed formulation to DEVS and to compare its behaviour with respect to the LSM. The results show that DEVS based wildfire propagation model qualitatively improves its performance (e.g., reproducing flank and back fire, increase in fire spread due to pre-heating of the fuel by hot air and firebrands, fire propagation across no fuel zones, secondary fire generation, \dots). Though the results presented here are devoid of any validation exercise and provide only a proof of concept, they show a strong inclination towards an intended operational use. The existing LSM or DEVS based operational simulators like WRF-SFIRE and ForeFire respectively can serve as an ideal basis for the same.Comment: Accepted for publication in Commun. Nonlinear Sci. Numer. Simula

We explore alternative formulations of the analogy between viable Horndeski gravity and Eckart’s first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that, upon performing the imperfect fluid decomposition, yields constitutive relations that can be mapped onto Eckart’s theory. We then investigate how different couplings to Einstein’s gravity, at the level of the field equations, can affect the thermodynamic formalism overall. Last, we specialize the discussion to the case of “traditional” scalar-tensor theories and identify a specific choice of the coupling function that leads to a significant simplification of the formalism.

We investigate the specific attenuation factor for the Bessel models of viscoelasticity. We find that the quality factor for this class can be expressed in terms of Kelvin functions and that its asymptotic behaviours confirm the analytical results found in previous studies for the rheological properties of these models.