A
common
and
effective
method
for
calculating
the
steady-state
distribution
of
a
process
under
stochastic
resetting
is
renewal
approach
that
requires
only
knowledge
reset-free
propagator
underlying
time
distribution.
The
widely
used
simple
model
systems
such
as
freely
diffusing
particle
with
exponentially
distributed
times.
However,
in
many
real-world
physical
systems,
propagator,
distribution,
or
both
are
not
always
known
beforehand.
In
this
study,
we
develop
numerical
to
determine
probability
positions
based
on
measured
system
absence
combined
We
apply
validate
our
two
distinct
systems:
one
involving
interacting
particles
other
featuring
strong
environmental
memory.
Thus,
can
be
predict
steady
state
any
system,
provided
free
it
undergoes
complete
resetting.
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(1)
Published: Jan. 3, 2025
We
investigate
the
granular
temperatures
in
force-free
gases
under
exponential
resetting.
When
a
resetting
event
occurs,
temperature
attains
its
initial
value,
whereas
it
decreases
because
of
inelastic
collisions
between
events.
develop
theory
and
perform
computer
simulations
for
gas
cooling
presence
Poissonian
also
probability
density
function
to
quantify
distribution
temperatures.
Our
may
help
us
understand
behavior
nonperiodically
driven
systems.
Journal of Physics A Mathematical and Theoretical,
Journal Year:
2024,
Volume and Issue:
57(24), P. 245001 - 245001
Published: May 15, 2024
Abstract
Partial
resetting,
whereby
a
state
variable
x
(
t
)
is
reset
at
random
times
to
value
ax(t)
,
overflow="scroll">0⩽a⩽1
generalizes
conventional
resetting
by
introducing
the
strength
as
parameter.
generates
broad
family
of
non-equilibrium
steady
states
(NESS)
that
interpolates
between
NESS
strong
=
0)
and
Gaussian
distribution
weak
→
1).
Here
such
processes
are
studied
from
thermodynamic
perspective,
mean
cost
associated
with
maintaining
derived.
The
phase
dynamics
implemented
potential
overflow="scroll">Φ(x(a→1
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(2)
Published: Feb. 1, 2025
We
investigate
the
first
passage
time
beyond
a
barrier
located
at
b≥0
of
random
walk
with
independent
and
identically
distributed
jumps,
starting
from
x0=0.
The
is
subject
to
stochastic
resetting,
meaning
that
after
each
step
evolution
restarted
fixed
probability
r.
consider
resetting
protocol
an
intermediate
situation
between
(r=0)
uncorrelated
sequence
jumps
all
origin
(r=1)
derive
general
condition
for
determining
when
restarting
process
0<r<1
more
efficient
than
jump.
If
mean
in
absence
larger
this
sufficient
establish
existence
optimal
0<r∗<1
represents
best
strategy,
outperforming
both
r=0
r=1.
Our
findings
are
discussed
by
considering
two
important
examples
jump
processes
which
we
draw
phase
diagram
illustrating
regions
parameter
space
where
some
optimal.
Entropy,
Journal Year:
2024,
Volume and Issue:
26(8), P. 665 - 665
Published: Aug. 5, 2024
We
consider
two
different
time
fractional
telegrapher's
equations
under
stochastic
resetting.
Using
the
integral
decomposition
method,
we
found
probability
density
functions
and
mean
squared
displacements.
In
long-time
limit,
system
approaches
non-equilibrium
stationary
states,
while
displacement
saturates
due
to
resetting
mechanism.
also
obtain
telegraph
process
as
a
subordinated
by
introducing
operational
such
that
physical
is
considered
Lévy
stable
whose
characteristic
function
distribution.
analyzed
survival
for
first-passage
problem
optimal
rate
which
corresponding
minimal.
Physical review. E,
Journal Year:
2024,
Volume and Issue:
110(2)
Published: Aug. 2, 2024
Fractional
heterogeneous
telegraph
processes
are
considered
in
the
framework
of
telegrapher's
equations
accompanied
by
memory
effects.
The
integral
decomposition
method
is
developed
for
rigorous
treating
problem.
Exact
solutions
probability
density
functions
and
mean
squared
displacements
obtained.
A
relation
between
fractional
equation
corresponding
Langevin
has
been
established
subordination
approach.
process
presence
stochastic
resetting
studied,
as
well.
An
exact
expression
both
nonequilibrium
stationary
distributions/states
Physical review. E,
Journal Year:
2024,
Volume and Issue:
109(6)
Published: June 21, 2024
The
discrete
stochastic
dynamics
of
a
random
walker
in
the
presence
resetting
and
memory
is
analyzed.
Resetting
effects
may
compete
certain
parameter
regimes,
lead
to
significant
changes
long-time
walker.
Analytic
exact
results
are
obtained
for
model
where
remembers
all
past
events
equally.
In
most
cases,
dominate
at
long
times
dictate
asymptotic
dynamics.
We
discuss
full
phase
diagram
resulting
due
effects.
Physical review. E,
Journal Year:
2024,
Volume and Issue:
110(4)
Published: Oct. 28, 2024
In
this
paper,
we
study
a
simple
model
of
diffusive
particle
on
line,
undergoing
stochastic
resetting
with
rate
r,
via
rescaling
its
current
position
by
factor
a,
which
can
be
either
positive
or
negative.For
|a|
<
1,
the
distribution
becomes
stationary
at
long
times
and
compute
limiting
exactly
for
all
1.This
symmetric
has
Gaussian
shape
near
peak
x
=
0,
but
decays
exponentially
large
|x|.We
also
studied
mean
first-passage
time
(MFPT)
T
(0)
to
target
located
distance
L
from
initial
(the
origin)
particle.As
function
x,
MFPT
(x)
satisfies
nonlocal
second
order
differential
equation
have
solved
it
explicitly
0
≤
1.For
-1
analytically
up
constant
κ
whose
value
determined
independently
numerical
simulations.Our
results
show
that,
(starting
shows
minimum
r
*
(a).However,
optimised
Topt(a)
turns
out
monotonically
increasing
demonstrates
compared
standard
origin
(a
0),
while
is
not
beneficial
search
target,
negative
is.Thus
followed
reflection
around
expedites
in
one
dimension.
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(4)
Published: April 7, 2025
We
consider
two
different
fractional
generalizations
of
the
heterogeneous
telegrapher's
process
with
and
without
stochastic
resetting.
Both
governing
equations
can
be
obtained
from
corresponding
standard
by
using
subordination
approach.
The
first-passage
time
problems
are
solved
analytically
for
both
models
finding
survival
probabilities,
densities,
mean
times.
showed
that
cases
there
optimal
resetting
rates
which
times
minimal.
present
work
carries
implications
toward
our
understanding
anomalous
diffusion
random
search
in
media.
Published
American
Physical
Society
2025
