Fluctuations in the presence of fields: Phenomenological Gaussian approximation and a class of thermodynamic inequalities

Abstract

The fluctuations of thermodynamic systems in the presence of the fields are considered. The approach is of phenomenological nature and developed in a Gaussian approximation. The cases of a magnetizable continuum in a magnetoquasistatic field, as well as the so called discrete systems are used to exemplify the study. In the latter case one finds that the fluctuation estimators depend both on the intrinsic properties of the system and on the characteristics of the environment. Following earlier ideas of one of the authors we present a class of thermodynamic inequalities for the systems investigated in this paper. In the case of two variables these inequalities are nonquantum analogs of the well known quantum Heisenberg "uncertainty" relations. In this context, the fluctuation estimators support the idea that Boltzmann's constant k has the signification of a generic indicator of stochasticity for thermodynamic systems.

Higher-order correlations for fluctuations in the presence of fields

“…By using the properties of the Jacobians the relation (25) can be transformed as follows: . Here is the place to point out that the result (28) is the same with the one obtained [1] within the Gaussian approximation. Now let us evaluate the second and third order parameters of fluctuations for the magnetic induction B.…”

“…As in previous work [1] (and above reminded) we consider a generalized system described by the set of extensive parameters (U, X 1 , X 2 , . .…”

Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions

“…Different parameterizations of η/s lead to different entropy production and therefore different final multiplicity, even if the initial state is kept the same. This is especially true for different parameterizations of the hightemperature shear viscosity, since most of the entropy is produced during the early stages of the collision [42]. We compensate this using different overall normalizations e.g.…”

Chemo-mechanical coupling in molecular motors interpreted through the uncertainty relations

“…(4) it follows that the respective quantities appear as a product of Boltzmanń s constant k B with non-stochastic expressions. Thus we can regard k B as a generic indicator of thermodynamic stochasticity, while Plancḱ s constant h is a generic indicator of quantum stochasticity, an idea first postulated in a different context by Dumitru and Boer [19].…”