Geometrical description of phase transitions in terms of diagrams and their growth function

Nonequilibrium thermodynamics. II. Application to inhomogeneous systems

We provide an extension of a recent approach to study nonequilibrium thermodynamics [Gujrati, Phys. Rev. E 81, 051130 (2010), to be denoted by I in this work] to inhomogeneous systems by considering the latter to be composed of quasi-independent subsystems. The system Σ along with the (macroscopically extremely large) medium Σ[over ̃] form an isolated system Σ0. The fields (temperature, pressure, etc.) of Σ and Σ[over ̃] differ unless at equilibrium. We show that the additivity of entropy requires quasi-independence of the subsystems, which results from the interaction energies between different subsystems being negligible so the energy also becomes additive. The thermodynamic potentials such as the Gibbs free energy that continuously decrease during approach to equilibrium are determined by the fields of the medium and exist no matter how far the subsystems are out of equilibrium, so their fields may not even exist. This and the requirement of quasi-independence make our approach differ from the conventional approach used by de Groot and others, as discussed in the text. We find it useful to introduce the time-dependent Gibbs statistical entropy for Σ0, from which we derive the Gibbs entropy of Σ; in equilibrium this entropy reduces to the equilibrium thermodynamic entropy. As the energy depends on the frame of reference, the thermodynamic potentials and the Gibbs fundamental relation, but not the entropy, depend on the frame of reference. The possibility of relative motion between subsystems described by their net linear and angular momenta gives rise to viscous dissipation. The concept of internal equilibrium introduced in I is developed further here and its important consequences are discussed for inhomogeneous systems. The concept of internal variables (various examples are given in the text) as variables that cannot be controlled by the observer for nonequilibrium evolution is also discussed. They are important because the concept of internal equilibrium in the presence of internal variables no longer holds if internal variables are not used. The Gibbs fundamental relation, thermodynamic potentials, and irreversible entropy generation are expressed in terms of observables and internal variables. We use these relations to eventually formulate the nonequilibrium thermodynamics of inhomogeneous systems. We also briefly discuss the case when bodies form an isolated system without any medium to obtain their irreversible contributions and show that this case does not differ from when bodies are in an extremely large medium.

Nuclear multifragmentation, percolation, and the fisher droplet model: common features of reducibility and thermal scaling

It is shown that the Fisher droplet model, percolation, and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42+/-0.02. The EOS Collaboration Au multifragmentation data yield barriers with a power-law exponent of 0.68+/-0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted.