Decrease in entropy as a result of measuring the time of escape from a potential well

The decrease in entropy when passing from an equilibrium thermodynamic system to a slightly nonequilibrium system is investigated. A quasi-equilibrium Boltzmann distribution is used to prove the conservation of free energy during this passage. Results are obtained for a Brownian particle in a potential well with a low escape probability. The escape is interpreted as a measurement. It is shown that because of the measurement itself, the distribution function is narrower than that for a system undisturbed by measurement, i.e., an equilibrium system. In this case, the entropy difference between the equilibrium and measurement-disturbed systems is equal to the amount of information entered into the system.     

Algebraic theory of the chemical potential and the condition of reactive equilibrium

Under the assumption that the time evolution of an infinite system in thermodynamical equilibrium commutes with a closed, connected proper subgroup of the full gauge group (reflecting the particle structure of the system), it is shown that the chemical potentials satisfy conditions of reactive equilibrium. In addition, it arises as a direct consequence of the compactness of the gauge group that the stoichiometric coefficients are integers.     

Two-slab all-optical spring

It is demonstrated that a waveguide consisting of two dielectric slabs may become an all-optical spring when guiding a superposition of two transverse evanescent modes. Both slabs are transversally trapped in stable equilibrium due to the optical forces developed. A condition for stable equilibrium on the wavenumbers of the two modes is expressed analytically. The spring constant characterizing the system is shown to have a maximal value as a function of the equilibrium distance between the slabs and their width.     

Fluctuations and stability of stationary non-equilibrium systems in detailed balance

A generalized thermodynamic potential for Markoffian systems with detailed balance and far from thermal equilibrium has been derived in a previous paper. It was shown that the principle of detailed balance is equivalent to a set of conditions fulfilled by this potential (“potential conditions”). The properties of this potential allow us to extend the validity of a number of thermodynamic concepts well known for systems in or near thermal equilibrium to stationary states far from thermal equilibrium. The concept of symmetry breaking phase transitions for these systems is introduced in analogy to thermal equilibrium systems by considering the dependence of the stationary probability density of the system on a set of externally controlled parameters {λ}. A functional of the time dependent probability density of the system is defined in close analogy to the Gibb's definition of entropy. This functional has the properties of a Ljapunov functional of the governing Fokker-Planck equation showing the stability of the stationary probability density. The Langevin equations connected with the Fokker-Planck equation are considered. It is shown that, by means of the potential conditions, generalized “thermodynamic” fluxes and forces may be defined in such a way that the smoothly varying part of the Langevin equations (kinetic equations) constitutes a linear relation between fluxes and forces. The matrix of coefficients is given by the diffusion matrix of the Fokker-Planck equation. The symmetry relations which hold for this matrix due to the potential conditions then lead to the Onsager-Casimir symmetry relations extended to systems with detailed balance near stationary states far from thermal equilibrium. Finally it is shown that under certain additional assumptions the generalized thermodynamic potential may be used as a Ljapunov function of the kinetic equations.     

Translation symmetry breaking in four dimensional lattice gauge theories

We consider lattice gauge theories with finite abelian groupG in the weak coupling regime. It is shown that there is only one translation invariant equilibrium state for the infinite system. In four dimensions we construct a nontranslation invariant equilibrium state, describing an infinite system with localized magnetic flux tube, starting and ending at infinity.     

Extremal properties of distribution function and statistical operator in equilibrium and nonequilibrium thermodynamics

It is shown that the distribution function and the statistical operator, in the case that the considered system is close to the equilibrium state, can be received by the method relying upon minimizing the information gain, which is connected with the transition of the system from a nonequilibrium state to the equilibrium state. For the systems far from equilibrium the nonequilibrium distribution function or the nonequilibrium statistical operator can be derived using a variational principle based on Jaynes' maximum entropy formalism including memory effects.     

Exact energy principle in magnetic reconnection for current-sheet models

On the basis of an exact nonlinear energy principle, it is shown that the change in magnetic topology (i.e., reconnection) in a finite-domain system leads to the conversion of magnetic field energy to particle energy. However, it is also shown that the conversion efficiency gradually disappears as the system size increases. This principle is demonstrated with model current-sheet equilibria including Harris and Fadeev solutions, as well as a current-sheet equilibrium which contains a singular current layer. The finding that energy conversion in reconnection is highly dependent on the system size may have an important implication for numerical simulations performed under finite geometry.     

Der harmonische Oszillator an der Oszillationsschwelle Untersuchungen unter dem Aspekt der Phasenübergänge

The harmonic oscillator with positive feed-back is a system far away from thermal equilibrium. Nevertheless, it can be treated as a thermodynamical system when replacing the temperature by the degree of feed-back. Thereby a kind of thermodynamical potentials can be calculated. At the oscillatory threshold all characteristics of 2nd or higher order phase transitions appear, stationary ones as well as dynamical ones. This is shown by calculations and experiments.     

Effects of the System Temperature on Dust Cluster Formation in Plasma

Effects of the system temperature on dust aggregation in plasmas are investigated using two‐dimensional molecular dynamics simulations. It is shown that as the system temperature increases, the boundary of the clusters becomes gradually irregular (i.e., deviating from sphere‐like), and the cluster system gradually changes from solid to liquid and finally to gas state. The mean square displacement, mean nearest‐neighbor distance in the clusters, cluster size and coupling parameter of the system are obtained and the properties of the system structure and dynamics are investigated. The time τ needed for reaching equilibrium for different temperatures is obtained. It is shown that τ firstly decreases and then increases with the temperature, indicating that there is an optimum temperature allowing a dust aggregation to reach an equilibrium state most rapidly. The simulation results agree qualitatively with the experimental observations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution

We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.     

Analytical thermodynamics. Part I. Thermostatics—General theory

A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained.     

A novel approach to the kinetic theory and hydrodynamic turbulence. II

A novel approach to the kinetic theory of gases is suggested through certain correlation functions known as product densities. This approach is shown to be very useful in explaining transitions from gaseous to liquid state as well as laminar to turbulent flows in gas dynamics. For large deviations from the equilibrium configuration, it is shown that the system obeys a set of generalised Navier-Stokes equation where some stochastic features are present.     

Stability of the normal phase in a bounded current-carrying superconducting film

The two-phase equilibrium states of a current-carrying thin superconducting film in the case of convective heat transfer on the free surface are considered, and their stability is investigated in a first approximation. It is shown that of the two equilibrium states, the state with the normalphase region of larger size is stable. In the limiting case of an infinitely long film, the stable two-phase equilibrium state tends to a spatially uniform normal state, and the unstable state remains localized. In a definite range of values of the system parameters, the relaxation time of such a formation can be fairly long, and it should be regarded as a quasistable equilibrium state. Zh. Tekh. Fiz. 68, 71–77 (June 1998)     

Impurity transport in a dual-porosity medium with sorption

A nonstationary model of impurity transport in a dual-porosity (fractured porous) medium with sorption is proposed. It is shown that the equilibrium between dissolved and adsorbed phases is absent for a prolonged time, which leads to the development of nonclassical impurity transport regimes. Parameter values are found for which the behavior of the system cannot be described using the conventional model of equilibrium sorption even at large times for which the equilibrium between dissolved and adsorbed components should be established.     

Comments on the equilibrium theory of the quantum hall effect

The relation between the thermal equilibrium Hall conductivity generated by minimal gauge transformation and the isolated Hall conductivity given by the Kubo formula is investigated. The contribution of the edge states and some general questions concerning the definition of the equilibrium Hall conductivity are discussed. It is shown that, in the case of an additive electron-impurity system, the two Hall conductivities coincide as long as the Fermi energy is situated in an energy gap.     

Equilibrium charge of small metal particles and hopping transport in a metal-insulator composite

It is shown that the thermodynamically equilibrium state of a system of small metal particles placed in a dielectric matrix are unavoidably charged. The charge of spherical metal particles with different radii is calculated at low temperatures. Hopping transport in a system of metal particles is studied. It is shown that it is limited by the charging energy, which serves as a typical hopping energy and can be gapless. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 510–515 (25 October 1999)