Explanation of the Gibbs paradox within the framework of quantum thermodynamics

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally looses its dominant place and the target of the paradox is naturally shifted to the decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of ``difference between the gases'' gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counter-intuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases, or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.Comment: Published version. New title. 17 pages Revte

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

The Socioeconomic Problems of Russian Science

The sharp decline in appropriations for science has been accompanied by the appearance of numerous proposals to reform the field of scientific research and development. Typical of these is a diminution of the role of the basic factors of the development of scientific potential (in particular state support, demand on the part of the science-intensive sectors of the economy, the provision of the necessary information resources for scientists, etc.) and exaggerated attention to factors that are secondary for the transitional period (venture financing of science-intensive technologies, the creation of technology parks and technology cities, etc.). A great danger to the further development of Russian science, primarily sector science, is posed by the proposals to eliminate sector and intersector budget allocations for scientific support (to a significant extent replacing the previously existing Unified Fund for the Development.

Analytical and Numerical Study of Equilibrium Characteristics of a Droplet with Charged Condensation Nucleus in the External Electric Field

Abstract -The equilibrium parameters of small dielectric droplet with charged condensation nucleus in the external uniform electric field are studied. Two typical cases are considered: (i) the droplet with charged nucleus suspended by external uniform electric field in the gravitational field and (ii) the droplet moves steadily under the action of external electric field with allowance for the resistance of surrounding vapor-gas medium. It is taken into account that the charged condensation nucleus can be displaced from the mass center of the droplet to new equilibrium position inside the droplet under the action of external electric field and response field. The scheme of the numerical solution of a nonlinear system of differential equations for the droplet equilibrium profile and electric potentials inside the droplet and in the vapor-gas medium at the arbitrary values of droplet size, strength of external field, and the charge of condensation nucleus is formulated and realized. Dependences of an equilibrium profile and the thermodynamic characteristics of a droplet such as the chemical potential of condensate and formation work on the droplet size, mass, and charge of condensation nucleus, the strength of external field and ratio of permittivities of droplet and the vapor-gas medium are plotted. Results of numerical calculations are supplemented by the analytical relations for equilibrium droplet characteristics in the first orders of the perturbation theory for a weak external field