Nonequilibrium phase transitions and pattern formation as consequences of second-order thermodynamic induction (original) (raw)
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Physical Review E, 2014
A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic variable depends on another thermodynamic variable then we have derived an expression that can predict the extent of the induction. The amount of induction is shown to be proportional to the square of the driving force. The nature of the intervariable coupling for the induction effect has similarities with the Onsager symmetry relations, though there is an important sign difference as well as the magnitudes not being equal. Thermodynamic induction adds nonlinear terms that improve the stability of stationary states, at least within the VKC class of systems. Induction also produces a term in the expression for the rate of entropy production that could be interpreted as self-organization. Many of these results are also obtained using a variational approach, based on maximizing entropy production, in a certain sense. Nonequilibrium quantities analogous to the free energies of equilibrium thermodynamics are introduced.
Journal of Physical Studies
We present study concerns a generalization of the model for extended stochastic systems with a field-dependent kinetic coefficient and a noise source satisfying fluctuation-dissipation relation. Phase transitions with entropy driven mechanism are investigated in systems with conserved and nonconserved dynamics. It is found that in stochastic systems with a relaxational flow and a symmetric local potential reentrant phase transitions can be observed. We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems of reaction diffusion kind. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. Our mean-field results are verified by computer simulations.
We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.
Nonequilibrium entropy and the second law of thermodynamics: A simple illustration
International Journal of Thermophysics, 1993
The objective of this paper is twofold: first, to examine how the concepts of extended irreversible thermodynamics are related to the notion of accompanying equilibrium state introduced by Kestin; second, to compare the behavior of both the classical local equilibrium entropy and that used in extended irreversible thermodynamics. Whereas the former does not show a monotonic increase, the latter exhibits a steady increase during the heat transfer process; therefore it is more suitable than the former one to cope with the approach to equilibrium in the presence of thermal waves.
Thermodynamics of entropy-driven phase transformations
Physical Review E, 2006
Thermodynamic properties of one-dimensional lattice models exhibiting entropy-driven phase transformations are discussed in quantum and classical regimes. Motivated by the multistability of compounds exhibiting photoinduced phase transitions, we consider systems with asymmetric, double, and triple well on-site potential. One finds that among a variety of regimes, quantum versus classical, discrete versus continuum, a key feature is asymmetry distinguished as a "shift" type and "shape" type in limiting cases. The behavior of the specific heat indicates one phase transformation in a "shift" type and a sequence of two phase transformations in "shape"-type systems. Future analysis in higher dimensions should allow us to identify which of these entropydriven phase transformations would evolve into phase transitions of the first order.
Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
Journal of Physics: Condensed Matter, 2013
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.
Entropy production of nonequilibrium steady states with irreversible transitions
Journal of Statistical Mechanics: Theory and Experiment, 2012
In nature stationary nonequilibrium systems cannot exist on their own, rather they need to be driven from outside in order to keep them away from equilibrium. While the internal mean entropy of such stationary systems is constant, the external drive will on average increase the entropy in the environment. This external entropy production is usually quantified by a simple formula, stating that each microscopic transition of the system between two configurations c → c with rate w c→c changes the entropy in the environment by ∆S env = ln w c→c − ln w c →c. According to this formula irreversible transitions c → c with a vanishing backward rate w c →c = 0 would produce an infinite amount of entropy. However, in experiments designed to mimic such processes, a divergent entropy production, that would cause an infinite increase of heat in the environment, is not seen. The reason is that in an experimental realization the backward process can be suppressed but its rate always remains slightly positive, resulting in a finite entropy production. The paper discusses how this entropy production can be estimated and specifies a lower bound depending on the observation time.
Pattern formation induced by nonequilibrium global alternation of dynamics
Physical Review E, 2002
We recently proposed a mechanism for pattern formation based on the alternation of two dynamics, neither of which exhibits patterns. Here we analyze the mechanism in detail, showing by means of numerical simulations and theoretical calculations how the nonequilibrium process of switching between dynamics, either randomly or periodically, may induce both stationary and oscillatory spatial structures. Our theoretical analysis by means of mode amplitude equations shows that all features of the model can be understood in terms of the nonlinear interactions of a small number of Fourier modes.
Four variants of theory of the second order phase transitions
Because of one-valued connection between the configurational entropy and the order parameter it is possible to present the theory of the second order phase transitions in terms of the configurational entropy. It is offered a variant of theory, in which the Nernst theorem is obeyed. Within the framework of heterogeneous model the phenomena of growth of level of fluctuations and their correlations are analyzed at transition of critical point as competitions of kinetic and relaxation processes in the conditions of proximity of two critical points.
Symmetries and nonequilibrium thermodynamics
Physical Review E, 2017
Thermodynamic systems can be defined as composed by many identical interacting subsystems. Here it is shown how the dynamics of relaxation toward equilibrium of a thermodynamic system is closely related to the symmetry group of the Hamiltonian of the subsystems of which it is composed. The transitions between states driven by the interactions between identical subsystems correspond to elements of the root system associated to the symmetry group of their Hamiltonian. This imposes constraints on the relaxation dynamics of the complete thermodynamic system, which allow formulating its evolution toward equilibrium as a system of linear differential equations in which the variables are the thermodynamic forces of the system. The trajectory of a thermodynamic system in the space of thermodynamic forces corresponds to the negative gradient of a potential function, which depends on the symmetry group of the Hamiltonian of the individual interacting subsystems.