Related papers: Deformed Density Matrix and Generalized Uncertaint…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
This work is an extension of the study into statistical mechanics of the early Universe that has been the subject in prior works of the author, the principal approach being the density matrix deformation. In the work it is demonstrated that…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of…
We present an exact treatment of the thermodynamics of physical systems in the framework of the generalized uncertainty principle (GUP). Our purpose is to study and compare the consequences of two GUPs that one implies a minimal length…
In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix…
We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function,…
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…
We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related…
We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such…
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the…
Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…