Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

The thermodynamics of Maxwell-Dilaton black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for the surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we construct a frame independent entropy from which we obtain a temperature which agrees with the standard results in the non-extremal regime, and has a desirable behaviour around the extremal configurations according to the third law of black hole mechanics.     

Some properties of generalized Fisher information in the context of nonextensive thermostatistics

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q$q$-Gaussian distributions and the q$q$-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed q$q$-entropy is attained, in both cases, by a generalized q$q$-Gaussian distribution. This complements the fact that the q$q$-Gaussians maximize the q$q$-entropies subject to a moment constraint, and yields new variational characterizations of the generalizedq$q$-Gaussians. We show that the generalized Fisher information naturally pop up in the expression of the time derivative of the q$q$-entropies, for distributions satisfying a certain nonlinear heat equation. This result includes as a particular case the classical de Bruijn identity. Then we study further properties of the generalized Fisher information and of their minimization. We show that, though non additive, the generalized Fisher information of a combined system is upper bounded. In the case of mixing, we show that the generalized Fisher information is convex for q≥1$q\ge 1$. Finally, we show that the minimization of the generalized Fisher information subject to moment constraints satisfies a Legendre structure analog to the Legendre structure of thermodynamics.     

On an adiabatic invariant in the thermodynamics of solids

A thermodynamic invariant in the form of the ratio of a vibrational frequency in an anharmonic solid to the temperature in adiabatic processes is derived. The adiabatic invariance established is used to derive in a simple manner an expression for the temperature change due to elastic adiabatic loading of solids (Kelvin's equation). Fiz. Tverd. Tela (St. Petersburg) 41, 134–136 (January 1999)     

Two-dimensional gravity with an invariant energy scale

We investigate the gauging of a two-dimensional deformation of the Poincaré algebra, which accounts for the existence of an invariant energy scale. The model describes 2D dilaton gravity with torsion. We obtain explicit solutions of the field equations and discuss their physical properties.     

Lorentz invariance with an invariant energy scale

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.     

Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general coordinate transformations in phase space are studied. It is argued that all relations expressing physical properties should be manifestly covariant, i.e. independent of the special system of coordinates used. The covariance of the Langevin-equations and the Fokker Planck equation is demonstrated. The diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space. Covariant drift vectors associated to the Langevin- and the Fokker Planck equation are found. It is shown that special coordinates exist in which the covariant drift vector of the Fokker Planck equation and the usual non-covariant drift vector are equal.The physical property of detailed balance and the equivalent potential conditions are given in covariant form. Finally, the covariant formulation is used to study how macroscopic forces couple to a system in a non-equilibrium steady state. A general fluctuation-dissipation theorem for the linear response to such forces is obtained.     

Geometrical aspects of a generalized statistical mechanics

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models. The thermodynamics of the system is the focus of attention in this geometric context.     

Dynamical trapping of particles as a challenge to statistical thermodynamics

A model of a dynamical trap is considered. This type of trapping appears as a result of reorganization of the trap surroundings (relaxation to a new local configuration) upon particle arrival. This can dynamically break existing overlaps of localized particle orbitals, i.e. to interrupt the return path for the particle. Thus, e.g., trapping at even a local potential maximum appears. The effect has nothing to do with, e.g., renormalization of particle energies owing to the bath. Scaling arguments are also presented to make the used kinetic treatment unquestionable.     

The invariant representation of generalized momentum

The relativistic-invariance representation of generalized momentum of a particle in the external field is proposed. In this representation the dependence of potentials of the particle-field interaction on the particle velocity is taken into account. An exact correspondence of expressions for the energy and potential energy for the classical Hamiltonian is established, which makes identical the solutions of problems of mechanics with relativistic and classical approaches. The invariance of the generalized momentum representation allows one to describe equivalently a physical system in geometrically conjugated spaces of kinematical and dynamical variables.     

On a kinetic justification of the generalized nonequilibrium thermodynamics of multicomponent systems

The problem of the kinetic justification of the generalized thermodynamics of nonequilibrium processes using the method of moments for solving the kinetic equation for a multicomponent gas mixture is examined. Generalized expressions are obtained for the entropy density, entropy flux density, and entropy production as functions of an arbitrary number of state variables (moments of the distribution function). Different variants of writing the relations between fluxes and thermodynamic forces are considered, which correspond to the Onsager version for spatially homogeneous systems and, in a more general case, lead to the generalized thermodynamic forces of a complicated form, including derivatives of the fluxes with respect to time and spatial coordinates. Some consequences and new physical effects, following from the obtained equations, are analyzed. It is shown that a transition from results of the method of moments to expressions for the entropy production and the corresponding phenomenological relations of the generalized nonequilibrium thermodynamics is possible on the level of a linearized Barnett approximation of the Chapman–Enskog method.     

On statistical thermodynamics of multicomponent systems II

The equivalent neighbour (EN) model of interacting continuous spherically symmetric spins with the length equal or smaller than unity is solved exactly for all values of the spin dimensionality, D. A surprising result is that only for D 628 the system undergoes phase transitions at temperatures lower than those of the EN model of interacting spins with the hypercubic symmetry. In the D → ∞ limit the equation of state in zero field is derived analytically and gives the Landau type behaviour in the whole range of temperatures.     

Correct thermodynamic forces in Tsallis thermodynamics: connection with Hill nanothermodynamics

The equivalence between Tsallis thermodynamics and Hill's nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the entropic index q which we illustrate with two physical examples, allowing in both cases to relate q to the underlying dynamics of the Hamiltonian systems.     

非完整约束奇异广义力学系统的Poincar-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系统 ,基于广义Apell_Четаев约束条件 ,并考虑到系统的内在约束 ,导出了该非完整约束奇异广义力学系统的广义Poincar _Cartan积分不变量 .并证明了该不变量与非完整约束奇异广义力学系统的广义正则方程等价     

New paradigm in thermodynamics and its connection with economics and linguistics

Our new approach to thermodynamics agrees with statistical laws of linguistics and economics.     

On the connection of nonequilibrium information thermodynamics with non-hamiltonian quantum mechanics of open systems

A critical and improved version of the non-Hamiltonian quantum mechanics and nonequilibrium information thermodynamics is presented. It has been shown that the latter is connected with the former through the set of macroscopical observables defining the additional conditions by maximization of information. This set of macroscopical observables occurs in the asymptotic solution of the equation of motion of the non-Hamiltonian mechanics if the latter is ergodic. The identity of the two sets of observables is the consistency condition of information thermodynamics of open systems. The general theory has been illustrated and discussed on two rigorously solvable examples. Using a $\text{C}{}^1\text{-}\text{algebraic}$ approach a connection has been shown with the results of field-theoretical axiomatic methods concerning the thermodynamical limit.