Kac ring model
E92908
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
→
model of irreversibility → statistical mechanics model → toy model → |
| analyzedUsing |
Markov chain methods
→
law of large numbers → probability theory → |
| assumes |
deterministic microscopic dynamics
→
discrete time steps → random initial distribution of scatterers → |
| demonstrates |
difference between microscopic reversibility and macroscopic irreversibility
→
role of probabilistic assumptions in thermodynamics → |
| describes |
evolution of binary variables as particles move around a ring
→
|
| field |
mathematical physics
→
statistical mechanics → |
| hasComponent |
binary variables on sites
→
ring of sites → scatterers on bonds or sites → |
| hasDynamics |
binary variable flips when passing a scatterer
→
particles move one site per time step around the ring → |
| hasIdealization |
binary spin-like degrees of freedom
→
non-interacting particles → |
| hasLimitation |
does not include genuine interactions between particles
→
irreversibility is only apparent and statistical → |
| hasMacroscopicBehavior |
irreversible
→
|
| hasMicroscopicDynamics |
time-reversible
→
|
| hasProperty |
exactly solvable
→
finite number of degrees of freedom → non-Hamiltonian idealization → |
| illustrates |
Boltzmann’s idea of molecular chaos
→
how coarse-graining leads to apparent irreversibility → law of large numbers behavior in many-particle systems → |
| introducedBy |
Mark Kac
→
|
| namedAfter |
Mark Kac
→
|
| relatedTo |
Boltzmann equation
→
H-theorem → Loschmidt paradox → Poincaré recurrence → kinetic theory → |
| shows |
entropy-like quantities can increase on average
→
recurrence at very long times for finite systems → |
| usedFor |
demonstrating time-reversal invariance at the microscopic level
→
illustrating macroscopic irreversibility → pedagogical explanation of the second law of thermodynamics → studying approach to equilibrium → |
| usedIn |
discussions of arrow of time
→
foundations of statistical mechanics → teaching thermodynamics → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Mark Kac
→
|
notableIdea |