相关论文: q-Legendre Transformation: Partition Functions and…
In this paper we introduce a kind of "noncommutative neighbourhood" of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless…
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arithmetic properties of KMS states in the corresponding quantum…
We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric algebra and show that it can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are…
In this paper, q-Laplace transforms related to the non-extensive thermodynamics are investigated by using the algebraic operation of the non-extensive calculus. The deformed simple harmonic problem is discussed by using the q-Laplace…
Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the…
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying…
The focus of this work is a correspondence between the Hilbert space operators on one hand, and doubly periodic generalized functions on the other. The linear map that implements it, referred to as the Q-transform, enables a direct…
We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
The paper deals with "quantization" and "second quantization" of phenomenological thermodynamics with respect to the Boltzmann's constant. It is suggested to perceive the quasithermodynamic parameter (corresponding to the Boltzmann's…
Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in(-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…