q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant

Details q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant

2009-12-29

arxiv.org/abs/0912.5302v2

Mathematics

Quantum Algebra

Scientific paper

In this paper we construct a q-analogue of the Legendre transformation, where q is a matrix of formal variables defining the phase space braidings between the coordinates and momenta (the extensive and intensive thermodynamic observables). Our approach is based on an analogy between the semiclassical wave functions in quantum mechanics and the quasithermodynamic partition functions in statistical physics. The basic idea is to go from the q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in thermodynamics. It is shown, that this requires a non-commutative analogue of the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the classical formulae. Being applied to statistical physics, this naturally leads to an idea to go further and to replace the Boltzmann constant with an infinite collection of generators of the so-called epoch\'e (bracketing) algebra. The latter is an infinite dimensional noncommutative algebra recently introduced in our previous work, which can be perceived as an infinite sequence of "deformations of deformations" of the Weyl algebra. The generators mentioned are naturally indexed by planar binary leaf-labelled trees in such a way, that the trees with a single leaf correspond to the observables of the limiting thermodynamic system.

Affiliated with

Also associated with

No associations

Rating

q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-62919