Here, we show that the fundamental Fickian process of diffusion can be equivalently described by a pressureless, compressible, and irrotational flow dynamics, whose effective force is governed by the divergence of the viscous stress tensor. This brings together the seemingly unrelated processes of mass and momentum transports.

1.
W.
Coffey
and
Y. P.
Kalmykov
,
The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering
(
World Scientific
,
2012
), Vol.
27
.
2.
R.
Tsekov
,
E.
Heifetz
, and
E.
Cohen
, “
Relating quantum mechanics with hydrodynamic turbulence
,”
Europhys. Lett.
122
,
40002
(
2018
).
3.
E.
Heifetz
,
R.
Tsekov
,
E.
Cohen
, and
Z.
Nussinov
, “
On entropy production in the madelung fluid and the role of bohm's potential in classical diffusion
,”
Found. Phys.
46
,
815
824
(
2016
).
4.
E.
Heifetz
and
E.
Cohen
, “
Toward a thermo-hydrodynamic like description of schrödinger equation via the madelung formulation and fisher information
,”
Found. Phys.
45
,
1514
1525
(
2015
).
5.
E.
Nelson
, “
Derivation of the schrödinger equation from newtonian mechanics
,”
Phys. Rev.
150
,
1079
(
1966
).
6.
P. K.
Kundu
and
I. M.
Cohen
,
Fluid Mechanics
(
Academic Press
,
2002
).
7.
U.
Frisch
and
J.
Bec
, “
Burgulence
,” in
New Trends in Turbulence Turbulence: Nouveaux Aspects
(
Springer
,
2001
), pp.
341
383
.
You do not currently have access to this content.