相关论文: Generalizing the Extensive Postulates

Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…

In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…

Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…

In his Comment [1], Philip Strasberg (PS) argues from the analysis of different examples that the framework we have presented in [2] does not recover known results of macroscopic textbook thermodynamics. Here, we show that such apparent…

Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…

We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios.…

The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…

It has been shown recently that Bose Gase with weak pair (enough well) interaction is non ergodic system. But Bose Gase with weak pair interaction is so general system that it is evident that the majority of statistical mechanics systems…

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…

Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…

Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…

We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures. This is obtained by proving a local central limit theorem and a local large…

We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…

Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…

Previous results on Renyi and Wang's formalism of the Tsallis thermostatics are founded by using an extensive variable z connected to the entropic parameter q. It is shown that in the thermodynamical limit both the Tsallis and Renyi…

We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…

Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…

In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…

At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…