In continuum physics, constitutive equations model the material properties of physical systems. those equations, symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with second law thermodynamics, which imposes that, any thermodynamic process, entropy production nonnegative....

In 1854 Clausius proved the famous theorem that bears his name by assuming the second "law" of thermodynamics. In the present paper we give a proof that requires no such assumption. Our proof rests on the laws of mechanics, a T-mixing property, an ergodic consistency condition, and on the axiom of causality. Our result relies on some recently derived theorems, such as the Evans-Searles and the ...

The natural outcome of the most striking similarity between the second laws of blackhole mechanics and thermodynamics is blackhole entropy. In this paper we discuss the evidence of blackhole entropy and the linearity relation between blackhole entropy to its horizon area. Finally, using thermodynamic relations we obtain Bekenstein-Hawking entropy, Hawking temperature and other intensive paramet...

In the present paper we consider the interacting holographic model of dark energy to investigate the validity of the generalized second laws of thermodynamics in non-flat (closed) universe enclosed by the event horizon measured from the sphere of the horizon named L. We show that for L as the system’s IR cut-off the generalized second law is respected for the special range of the deceleration p...

We set up a discrete space-time dynamical model of molecules with thermalised kinetic energy and repulsive cores, in an external potential. The model obeys the first and second laws of thermodynamics. The continuum limit, obtained using a MAPLE program, gives rise to coupled reaction-diffusion equations for the density and temperature fields. The system obeys Onsager symmetry and exhibits the S...

The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized formalism is created by expansion of the canonical Hamilton's formalism to the open systems. A formula, which expresses the entropy through the work of subs...

The classical first law of thermodynamics for a Kerr-Newman black hole (KNBH) is generalized to a law in quantum form on the event horizon. Then four quantum conservation laws on the KNBH equilibrium radiation process are derived. The Bekenstein-Hawking relation S = A/4 is exactly established. It can be inferred that the classical entropy of black hole arises from the quantum entropy of field q...

where r is a constant, models the thermal behaviour of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed by Lane (1) (see also (3)) and studied in detail by Emden (2). Fowler (4; 5) considered a generalization of Eq. (1), called Emden-Fowler equation (6), where the last term is replaced by...

In this paper we derive thermodynamically consistent higher order phase field models for the dynamics of vesicle membranes in incompressible viscous fluids. We start with basic conservation laws and an appropriate version of the second law of thermodynamics and obtain generalizations of models introduced by Du, Li and Liu [5] and Jamet and Misbah [13]. In particular we derive a stress tensor in...