# Dynamical evolution in non-commutative discrete phase space and the derivation of classical kinetic equations

@inproceedings{Dimakis2000DynamicalEI, title={Dynamical evolution in non-commutative discrete phase space and the derivation of classical kinetic equations}, author={Aristophanes Dimakis and Constantinos Tzanakis}, year={2000} }

By considering a lattice model of extended phase space, and using techniques of non-commutative differential geometry, we are led to: (a) the concept of vector fields as generators of motion and transition probability distributions on the lattice; (b) the emergence of the time direction on the basis of the encoding of probabilities in the lattice structure; (c) the general prescription for the evolution of the observables in analogy with classical dynamics. We show that, in the limit of a… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

## DISCRETIZATION AND MOYAL BRACKETS

VIEW 1 EXCERPT

CITES METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 49 REFERENCES

## Introduction to noncommutative geometry of commutative algebras and applications in physics

VIEW 1 EXCERPT

## Introduction to noncommutative geometry of commutative algebras and applications in physics ” in

## Some aspects of noncommutative geometry and physics

VIEW 1 EXCERPT