Sustainable Evolution in an Ever-Changing Environment

It is suggested that the notion of equation-of-state serves as appropriate common basis for studying the macroscopic behavior of both traditional physical systems and complex systems. The reason is that while the equilibrium systems are characterized both by their energy function and the corresponding equation-of-state, the steady states of out-of-equilibrium systems are defined only by their dynamics, i.e. by their equations-of-state. It is demonstrated that there exists a common measure which generalizes the notion of Gibbs measure so that it acquires two-fold meaning: it appears both as local thermodynamical potential and as probability for robustness to environmental fluctuations. It is proven that the obtained Gibbs measure has very different meaning and role than its traditional counterpart. The first one is that it is derived without prerequisite requirement for simultaneous achieving of any extreme property of the system such as maximization of the entropy.

Equilibrium Nonlinear Distributions of One-Component Order Parameter in Systems with Competitive Interaction

The approach which enables to obtain the solutions of the variational equation as the series [Formula: see text] is considered. It is shown that when N=1 it gives well-known cos x solutions, while for N>1 it leads to essentially nonlinear functions. The φ2φ′2-term in the thermodynamical potential provides the proper nonlinear behavior of the order parameter and the possibility of existence of kink-like distributions, particularly. In special case N=2 there exist the exact partial solutions which, however, do not give the absolute minima to the thermodynamical potential.

1/Nc EXPANSION FOR THE PARTITION FUNCTION IN FOUR-FERMION MODELS

We present a derivation of the bosonic contribution to the thermodynamical potential of four-fermion models by means of a 1/N c -expansion of the functional integral defining the partition function. This expansion turns out to be particularly useful in correcting the mean field approximation especially at low temperatures, where the relevant degrees of freedom are low-mass bosonic excitations (pseudo-Goldstones).