相关论文: Thermodynamics and time-average

The Boltzmann--Gibbs entropy is a functional on the space of probability measures. When a state space is countable, one characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity,…

Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…

We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…

The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations…

A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…

In this paper, we extend Gibbs's approach of quasi-equilibrium thermodynamic processes, and calculate the microscopic expression of entropy for general non-equilibrium thermodynamic processes. Also, we analyze the formal structure of…

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…

What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we…

There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…

For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…

We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy functionals with a single parameter $q$. These reduce to the extensive Boltzmann-Gibbs form for $q=1$, but…

The aim of the present paper is to present a careful and accessible discussion of the formal aspects of Boltzmann-Gibbs and Tsallis entropies. We begin with a brief overview of Boltzmann-Gibbs entropy, highlighting its main properties and…

A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states…

It is shown that the Gibbs paradox is actually paralogism, viz. an erroneous statement sounding credible due to the statistic-mechanical interpretation of entropy as a measure of "any and all" irreversibility. As an alternative, the…

We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…