Transport coefficients
|
η |
shear viscosity |
|
λ |
thermal conductivity |
|
ηV |
bulk viscosity |
|
ζ |
Brownian friction coefficient |
|
D |
self diffusion coefficient |
Thermodynamic fluxes
|
P |
the pressure tensor |
|
JQ |
heat flux |
|
Π |
viscous pressure tensor |
Thermodynamic forces
|
∇u |
strain rate tensor |
|
γ |
shear rate = ∂ux∕∂y |
|
∇T |
temperature gradient |
|
∇.u |
dilation rate |
|
u |
streaming velocity |
|
ε |
elastic deformation |
|
∇ε |
strain tensor |
|
|
dilation rate = ⅓ |
Thermodynamic state variables
|
T |
temperature |
|
kB |
Boltzmann's Constant |
|
β |
1∕kBT |
|
V |
volume |
|
p |
hydrostatic pressure, = ⅓ tr(P) |
|
N |
number of particles |
|
ρ |
mass density |
|
n |
number density |
Thermodynamic constants
|
G |
shear modulus |
|
CV |
constant volume specific heat |
|
Cp |
constant pressure, specific heat |
|
cv |
constant volume,specific heat per unit mass |
|
cp |
constant pressure,specific heat per unit mass |
|
DT |
isochoric thermal diffusivity |
Thermodynamic potentials
|
E |
internal energy |
|
U(r,t) |
internal energy per unit mass |
|
S |
entropy |
|
s(r,t) |
internal energy per unit volume |
|
σ |
entropy source strength = rate of spontaneous entropy production per unit volume |
|
I |
enthalpy |
|
Q |
heat |
Mechanics
|
L |
Lagrangian |
|
H |
Hamiltonian |
|
H0 |
phase variable whose average is the internal energy |
|
I0 |
phase variable whose average is the enthalpy |
|
J(Γ) |
dissipative flux |
|
Fe |
external field |
|
α |
thermostatting multiplier |
|
iL |
p-Liouvillean |
|
iL |
f-Liouvillean |
|
A † |
Hermitian adjoint of A |
|
Λ |
phase space compression factor |
|
expR |
right time-ordered exponential |
|
expL |
left time-ordered exponential |
|
UR(t1,t2) |
incremental p propagator t1 to t2 |
|
UR(t1,t2)-1 |
inverse of UR(t1,t2), take phase variables from t2 to t1, UR(t1,t2)=UL(t1,t2) |
|
UR(t1,t2) |
incremental f propagator t1 to t2 |
|
TR |
right time-ordering opertator |
|
TL |
left time-ordering opertator |
|
CAB(t) |
equilibrium time correlation function = ⟨A(t)B*⟩ |
|
[A,B] |
commutator bracket |
|
{A,B} |
Poisson bracket |
|
δ(t) |
Dirac delta function (of time) |
|
δ(r-ri) |
Kirkwood delta function |
|
=0, |r-ri|> an infinitesmal macroscopic distance, l |
|
|
=1∕l3, |r-ri|< an infinitesmal macroscopic distance, I |
|
|
f(k)=∫dreik⋅rf(r) |
spatial Fourier transform |
|
f(ω)=∫∞0dre-iωtf(t) |
temporal Fourier-Laplace transform ∏ |
|
dS |
infinitesmal vector area element |
|
J⊥ |
transverse momentum current |
|
ϕ |
total intermolecular potential energy |
|
ϕij |
potential energy of particle i,j |
|
K |
total kinetic energy |
|
fc |
canonical distribution function |
|
fT |
isokinetic distribution function |
|
m |
particle mass |
|
ri |
position of particle i |
|
rij=rj-ri |
|
|
vi |
velocity of particle i |