Quasilocal equilibrium condition for black ring

We use the conservation of the renormalized boundary stress-energy tensor to obtain the equilibrium condition for a general (thin or fat) black ring solution. We also investigate the role of the spatial stress in the thermodynamics of deformation within the quasilocal formalism of Brown and York and discuss the relation with other methods. In particular, we discuss the quantum statistical relation for the unbalanced black ring solution.Comment: v2: refs. added, matches the published versio

Arbitrage and Equilibrium in Economies with Externalities.

We introduce consumption externalities into a general equilibrium model with arbitrary consumption sets. To treat the problem of existence of equilibrium, a condition of no unbounded arbitrage, extending the condition of Page (1987) and Page and Wooders (1993, 1996) is defined. It is proven that this condition is sufficient for the existence of an equilibrium and both necessary and sufficient for compactness of the set of rational allocations.CONSUMPTION ; EXTERNALITIES ; ARBITRAGE

Dynamic critical exponent of two-, three-, and four-dimensional XY models with relaxational and resistively shunted junction dynamics

The dynamic critical exponent $z$ is determined numerically for the $d$-dimensional XY model ($d=2, 3$, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of $z$ are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the the same boundary condition do not always give the same value of $z$. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of $z$ consistent with expectations for superfluids and superconductors: $z = 2$, 3/2, and 2 for $d=2$, 3, and 4, respectively.Comment: 21 pages, 16 figures, final versio

On the equilibrium concept for overlapping generations organizations

A necessary feature for equilibrium is that beliefs about the behavior of other agents are rational. We argue that in stationary OLG environments this implies that any future generation in the same situation as the initial generation must do as well as the initial generation did in that situation. We conclude that the existing equilibrium concepts in the literature do not satisfy this condition. We then propose an alternative equilibrium concept, organizational equilibrium, that satisfies this condition. We show that equilibrium exists, it is unique, and it improves over autarky without achieving optimality. Moreover, the equilibrium can be readily found by solving a maximization program.Economics ; Equilibrium (Economics) - Mathematical models

Off-equilibrium confined dynamics in a glassy system with level-crossing states

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when the temperature is varied. We give a full description of this constrained out of equilibrium behavior and we clarify the connection to the thermodynamics by computing (sub-dominant) TAP states, constrained to the starting equilibrium configuration.Comment: 10 pages, 3 figures; longer version with appendi

A necessary condition for the thermalization of a quantum system coupled to a quantum bath

A system put in contact with a large heat bath normally thermalizes. This means that the state of the system approaches an equilibrium state, the latter depending only on macroscopic characteristics of the bath (e.g. temperature), but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present paper we concentrate on one aspect of thermalization, namely, on the system initial state independence (ISI) of the equilibrium state. A necessary condition for the system ISI is derived in the quantum framework. We use the derived condition to prove the absence of the system ISI in a specific model. Namely, we consider a single spin coupled to a large bath, the interaction being of a specific form. Although the model under consideration is nontrivial enough to exhibit the decoherence and the approach to equilibrium, the derived necessary condition is not fulfilled and thus the equilibrium state depends on the initial state of the spin.Comment: v.2: The paper is substentially revised. Additional results are presented. The discussion of an exactly solvable model is added, the numerical calculations are removed; v.3: minor improvement