Dynamics of Markovian Particles
Encyclopedia
Dynamics of Markovian particles (DMP) is the basis of a theory
for kinetics
of particles
in open heterogeneous systems. It can be looked upon as an application of the notion of stochastic process
conceived as a physical entity; e.g. the particle moves because there is a transition probability acting on it.
Two particular features of DMP might be noticed: (1) an ergodic-like relation between the motion of particle and the corresponding steady state
, and (2) the classic notion of geometric volume
appears nowhere (e.g. a concept such as flow of "substance" is not expressed as liter
s per time unit but as number of particles per time unit).
Although primitive, DMP has been applied for solving a classic paradox
of the absorption of mercury
by fish
and by mollusks. The theory has also been applied for a purely probabilistic
derivation of the fundamental physical principle: conservation of mass
; this might be looked upon as a contribution to the old and ongoing discussion of the relation between physics
and probability theory
.
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
for kinetics
Kinetics (physics)
In physics and engineering, kinetics is a term for the branch of classical mechanics that is concerned with the relationship between the motion of bodies and its causes, namely forces and torques...
of particles
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
in open heterogeneous systems. It can be looked upon as an application of the notion of stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
conceived as a physical entity; e.g. the particle moves because there is a transition probability acting on it.
Two particular features of DMP might be noticed: (1) an ergodic-like relation between the motion of particle and the corresponding steady state
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...
, and (2) the classic notion of geometric volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
appears nowhere (e.g. a concept such as flow of "substance" is not expressed as liter
Litér
- External links :*...
s per time unit but as number of particles per time unit).
Although primitive, DMP has been applied for solving a classic paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
of the absorption of mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
by fish
Fish
Fish are a paraphyletic group of organisms that consist of all gill-bearing aquatic vertebrate animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish, as well as various extinct related groups...
and by mollusks. The theory has also been applied for a purely probabilistic
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
derivation of the fundamental physical principle: conservation of mass
Conservation of mass
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system will remain constant over time...
; this might be looked upon as a contribution to the old and ongoing discussion of the relation between physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
.