SCIENTIFIC ABSTRACT STRATONOVICH, R.L. - STRATU, Z.A.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001653510003-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 3, 2016
• Document Release Date: August 26, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

88440
S/056/60/039/006/071/063
Boo6 B056
AUTHOR: Stratonovich, R. L.
TITLE: Fluctuation Thermodynamics of 17onequilibrium Processes
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1960,
Vol. 39, 11o. 6(12), pp. 1647-1659
TEXT: Hitherto, the most important results obtained in the field of the
quantum thermodynamics of nonequilibrium processes have been obtained by
using perturbation-theoretical methods. In the present paper, a relation
is derived between the two-dimensional characteristic function of the
statistical equilibrium fluctuations and the one-dimensional characteristic
function (distribution function) of the nonequilibrium process without
using the perturbation theory. For the purpose of deriving this relation,
the quantum-theoretical apparatus developed by Feynman (Ref. 5) is used.
I
The relation obtained is (9):
0 8
exp Equilibrium at the temperature T n 1/kA
4' 3kTu'
Card 1/3

88440
Fluctuation Thermodynamics of Yon- S10561601039100610311063
equilibriui.,l Processes B006/B056
is determined by the density matrix eW-Aff, where'YE Y (T,a)
__ _(~71In Sp e- r1H the free energy, a thermodynamical parameter, the other
parameters being defined as usual (cf. Ref- 5), and the Feynman relation
e-f~H+uF = exp A(H)s + u(F) ds3 holds. This universal relation (9)
between the equilibrium distribution of the fluctuations and the non-
equilibrium fluctuation processes leads to a number of new results. In
the transition to one-dimensional distribution, an important formula is
obtained, which furnishes the quantum generalization of the theory of
equilibrium functions by V, B. Magalinskiy and Ya. P, Terletskiy. From
(9) it is possible, by differentiation, to derive Callen's equation in
the theory of non-equilibrium fluctuations. By means of (9) it is further
possible to investigate a phenomenon of basic interest, called "residual
correlations", which consists in the fact that in the case of equilibrium
fluctuations, the correlations between the values of thermodynamical
parameters do not vanish if the interval of time is increased; thus, this
is a case of non-ereodicity. The residual correlations and the non-
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88440
Fluctuation Thermodynamics of B'on- S10561601039100610311063
equilibriur.a 1'rocez;3es B006/3056
erGodicit,, , coefficient introduced can be expressed by the thermodynLimical
functions of Mae _,ystev.. In the case of a proportional increase of the
volume of '..:c ,;,iste,,.-. and of the number of particles it contains, residual
correlrl'.'on~- .-1: 1. non-cr&odicity coefficient remain finite. If the prin-
ciplo of 'U~c. reveisibilitty of the time axis is applied to (9), the
reciprocitL- conditions may be derived herefrom. As, in this case, the
-mallno-zi c' ~1,c ~crturbation is not assumed, the deviation of the non-
equilibriu,:. ~;rocess from the equilibrium process need not necessarily be
small, an(: ",-o equation describing a rela,,cation yrocess need not neces-
sarily be lin,:ar (OnsaGer equation). It is shown how the Onsaf;er relations
can be extended to nonlinear nonequilibrium processes. V. V. Vladimirskiy
is mentioned. There are 9 references: 4 Soviet and 5 US.
AS:XCIA'.'IO1.: Eo,;kovskiy gosudarstvennyy universitet (Moscow state
Unjiversity)
SUB11ITT'_D: May 25, 1960
Card

STRATONOVICIII -, It'L ; KIM-1011TOVICH, Yu.L. , nauchnyy red., dots.; IVAIIUSHKO,11.D..,
. --. SVESIR,'IKOV, A.A., tekhn. re,1.
(Selected problems concerning the theory of fluctuations in radio
engineering] lzbrannye voprosy teorli fliuktuatsii v radiotekhnike.
1,/joskva, Izd-vo "Sovetskoe radio," 1961. 557 p. WIRA 14:12)
(Radio)

S/024/61/000/002/011/014
E.140/E113
A =IHOR: Stratonov-ich,_JLj, (Moscow)
TITLE: Conditional distribution of correlated random points
and utilization of the correlation for the optimal
detection of a pulse signal in noise
PERIODICAL: Izvestiya Akademii nauk SSSR, otdeleniye tekhnicheskikh
nauk, Energetika i avtomatika, 1961, No.2, pp.148-158
TEXT: The author considers the general problem of a variable
number of pulses with correlation between given pulses in the
train and shows that utilization of the a priori knowledge of the
correlation permits improved detection of pulses in noise.
Let A denote the event in which there are n random points in
the signal, displaced a small amount from their true positions in
the signal. Then the conditional density distribution for the
signal with noise for the event A can be used, with suitable qJ6
passage to the limit of zero displacement, to determine the
conditional probability for the n points and this in turn leads
C, to the a posteriori distribution function. A number of results
given in an appendix are involved in the derivation. Two examples
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S11811611003161010081036
)"I'M 0161 M/ 7,116 B102/B108
AUTHORt Stratonovizh,_R~~
TITLEt Statistics of magnetizatidn in the Iaing model
PERIODICALs Fizika tverdogo tela, v- 31 no. 10, 1961, 2955 --~ 2966
TEXTs The magnetization probability distribution is calculated for a
bounded one-dimensional anisotropic crystal oonsisting of chain moleoules.
In the Ising modelp the free energy in suoh a crystal, f(H) --row - MHO
is represented as a statistical sum: Z(H) = en"W. M - -avai is the
magnetization (the extensive inner parameter), K - the field strength (the
intensive outer parameter), t(H) - the free Gibbs energy, Ir (M) the free
0
Helmholtz energytp - (kT)-'. The sought magnetization-probability
distribution dons ty is given in Fourier representation by.
j,j( Z(H-*-ikTv) dv.
e- Me
2n

29686 S/18 61/003/010/008/036
Statistics of magnetization... B102YB108
The Hamiltonian of a one-dimensional Ising chain is given by
N-I Ar
'V = -j I ISA-I.-I - 11 - ~H I Si. (9)
where ?8 are the components of the dipole moment of the elementary
dipole. For N dipoles,Z(H)= chj-o- -x-'-sh2j A"-' -i- ch x -#- sh2
V;hjt -I Vshl il -+- xt
A c h 71eS-1 12 -,q - -,- 4-T;
X = e-10j, 'I = PI"M
results from exact calculation. ZI(H) -A N + AN or, approximately#
Z' (H) - exp[pmoflly~H-7-1 + exp r-AM VrH +7 (17) holds for a dipole chain
H +H 01 0 1
0 V V
forming' a loop. By means of these formulas, the distribution density (7)
is calculated with the new variable p - PH + iv.
Card 2

25U6 S/181/61/003/0'10/008/036
Statistics of magnetization... B102/B108
11T5 - M2
W M == -L -I. ( I/ ~~ - ) -f- - -4-
Mk Mk Afk vk'~-~M' Mk
(25)
is found, and, with the aid of (17),
W M MO M`)
F(-H) Mkj1M-1 10
I O-Mv
for a closed chain.
-+- a (M MO) (M -f- MO)
Mo ~iN, Ho kTx/4.
(26~
The probability for all
dipoles to have positive (or negative) orientation is given by 'ZO(H)
(M - +M ), or, for a closed chain eP MH /Z'(H). In the followingp the
0
author derives and'diecusees asymptotic formulas for the probability
dard 31

Statistics of magnetization...
distribution with large M . With f, (H)
0 as
Z,YUUU S/181/61/003/010/008/036
B102/BJ08 mean
- -M~fHr+ (kT/M.)
fMO"-K
It (M)
-(kT/Mk)
-
magnetization of the correlation region) and
iv as
W(M) exp[pl"(H) +PMH -Alr
O(M)] is found with
e 211
F(M)-t-
-No (-V-MT (37)
e- E-3- VM,2, - M2 'tm,
F(M)= j -Mt V'jjo~,V2
-ya
ThiB function has three minima and, at large M, increases as
kT (M2+2M0M); (1 2 . kTM0p/x. For a region which may be considered as
2o2 -
belonging to an infinite chain
w(M=C;-Ieojw["-4--VH--t.-HO2-L-Ha f(M. (41).
kT ORD am]
=h H exp [=fz PAIH-- PM. (42)
2
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29686
S/181/61/003/010/008/036
Statistics of magnetization... B102/B108
is found. N denotes the number of adjacent dipoles and M their total
magnetization. Multiple magnetization correlations are investigated by
means of the theory of the Markov procesees. Approximate formulas are
derived for a finite closed chain. In the last chapter the author
discusses the applicability of the results to other systems with long-
range interaction. The author thanks V. L. Ginzburg for discussions.
There are 7 references, 4 Soviet and 3 non.-Soviet. The two references
to English-language publications read as followst G. F. Newell,
E. W. MontToll. Rev. Mod. Phys., 25., 353, 1953; C. Domb. Adv. in Phys.,
9, 149r 1960; B. Kaufmanq L. Onsager. Phys. Rev., 1_6- 8, 1244, 1949-
ASSOCIATION: Moskovskiy gosudarstvennyy universitet im. M. V. Lomonosova
(MoBcow State University imeni M. V. Lomonosov)
SUBMITTEDt April 10, 1961

KUM171"OVY P.I.; STPUTOYOVIC11, R.L.; TI.,UIGI.'OV, V.I. (Iloscow)
Some problems involving conditional prol- '1--ty and quasi-
moment functions. Teor. veroiat. i cc 6 no.4:458-,164
161. (n= a4:11)
(Probabilities)

AUTHOR:
TITLE:
Stratonovich, R.L.
2h865 S/109/61/006/007/005/020
D262/D-4;06
Optimal reception of a narrow band signal of unknovm
frequency on a background of noise
PERIODICAL: hadiotekhnika i elektronikat v. 6, no. 7P 1961#
1063 - 1075
TEXT: In the present artuicle, optimal receiving sy-stems are propo-
sed. These are designed using the principle of keeping track of the
most probable value of the signal frequency. For this purpose a fre-
quency discriminator with feedback could be used. The optimum amount
of feedback is determined theoretically from the equations of opti-
mum detection. This value varies because of the varying information.
Another property of the system is that detuning L from resonant fre-
quencies of the discriminator circuits is not in direct dependence
on the time ol" the a priori deterir~ined variation of frequency and
on the damping of the ccts. There are, however, certain difficul-
ties related to the start of observations. At this instanT the fore-
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24'65 6/109/61/006/007/005/02C)
Optimal reception of a ... D262/D306
quency may be far fron predicted and the ByStC-M Will initially ope-
rate in a non-optir,,lal regime. These difficult.Jes are omitted in the
present article. It is assumed that the initial determination of
Prequency is achieved using e.G. the system of parallel circuits
(Ref, 3: Yu.B. Chernyakj obnarusheniye signala s neizvestnoy chas-
totoy i proizvollnoy nachallnoy fazoy na fone belogo shuma, Radio-
tekhnika i elektronika, 1960, 5,3, 366). The proposed system is
then connected, the frequency determined i-nore accurately and its
changes followed. The system works in a non-stationary regime.
First the dposteriori probability density of frequency is deterni-
ned. Initially tle signal parameters are assumed constant and hav-
ing the apriori distribution density
w (A, cp 9 (,,) = -1 vi (A) vi (W) -
pr 21t pr Pr
The distorted signal r(t) = s(t) + n(t) is received during time
0 < t--_ T. After reception frequency w becomes a random quantity,
determined by the a posteriori distribution density w Ps (w, T) which
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I % 24865 S/109/61/006/007/005/020
Optimal reception of a ... . D262/D306
has to be determined. If the noise n(t) is a 14arkov process thbn
there is a corresponding functional of probability 17Ln(t))&' Since
the signal is statistically independent of noise the joint distri-
bution of signal parameters can be written as
const wpr w) VI[n(t)
from which the aposteriori distribution of signal parameters has*
the form of
17 ps (A,cf, w) = const wpr (A, cp, w) 'W[r(t) co.s('Wt + (2)
To obtain the aposteriori distribution for frequency Eq. (1) has to
be considered and (2) integrated with respect to A andcP&-Several*i
particular cases are then given. It is stated in conclusion that
the described system is not ideal. This is so because
d I da M (too, T) 8
&VT
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S/109/61/006/OQ7/005/020
Optimal reception of a ... D262/D306
in particular is approximate only representing the first equation
of pL more complicated system, but the gorresponding error is the
smaller, the greater the accuracy of the:aposteriori evaluated fre-
quency. ~Abstractorfs note; Eq. (28) is the eration of optimum..,fil-
tration (detection) in Gaussian.approximation - The author acknow-
ledges the interest taken in his-work by Yu.B. Kobzarev and.-A.Ye.
Basharinov. In the two appendices the mathematical analysis is.given
of the aposteriori probability with the correlated noise as given
in 23'q. (2) and also that with fluctuating noise. There are 2 figu-
res and 5 references: 4 Soviet-bloc and 1 non-Soviet-bloc. The re-
ference to the English-language publicatiq reads as follows: P,.
Bello, Joint estimation of delay, Doppler-and Doppler ratet IRE'
Trans., 1960, IT-6, 3, 330.
SUBMITTBD: April 28, 1960
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20
S/10)'/61/000-/009/003/018
D20i/D302
AUTHORS: Kul'man, N.K., an.1 Stratonovich, R.L.
TITLE: Certain optimum i11,11tililatiOnS fcr detecting a pulse
signal (if i-andoin duration in the presence of noise
PERIODICAL: Ridiotekhnika i ell-ektronika, v. 6, no. 9, 1961,
1442 - 1451
TEXT: It is assumed tha-~ tho usoful oignal ii a Markov proceas,
i.e. the time during whicli trie aignal remains in each of its possi-
ble states has an exponentJ~al a priori law of distribution. When
considering a stationary problem, the optimum filter may also be
designed from the linear Kolmogorov-Wiener theory, but it will be
14
worse than the non- Anear system, designed according -to -the !ilarkov
theory, since according to the former an optimum system has to be
bound in the class of linear ones, while the real optimum system
is non linear. The theoretical expansion of those systems is mathe-
matically rather difficuit, jo that the auth-l-,ra restrict their ana-
iysis and coraparisoll t-1 an assyletrical signa! and a small noise L9
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S/!;_)q/61/ 006/009/003/013
Certain opt-,aLum D,: O'L / D3 01 1~'
level. They prove 'tha,~ in asp of' f -.1 te ring-.:,,,At of a strongly assy-
mmetrical rectangular and random signal fr:)m tle background of
white noise, the optimum non-iin4~ar and linear kilters are charac-
terized by false s,,gna__. del~,_-:On and non-detf~ction. Filtering of
a generalized tdiegraph-ir slt,~,nal _9 consIdered composed o", a trei-n
of rectangular I)ulsc,% wY,,Io -),. may have values -ta and -a. The pulses
have a given number a ar--~ (I of Transitions fr'Dm -a state into -a((X)
4
and from -.a into -ta(V). Th~~ noise :Ls als.1111AMed to be white noif3e with
a spectra' density N( T' The a priori probabilities
w+_ and w are states -a and --a -and satisfy therefore
,k~ aw" - Bw_ . ;I- = aw +~ - Ow-'.
The signal represents ihus a Markov process. The foilowing equation
for optimum filtering, in aimensionless parameters is then ob-
tained:
dz (T
Card 2/5 dt Q

2 j-1 5 2c
S'/',Oq /6!/'006/009/003/018
Certain optimum installations ... D201/XO2
In it z(t W_" (t w- (t ), where w" the a posteriori pro-
0 Ps 0 ps 0 Ps
bability of the signal being in state +a, wp, - a posteriori proba-
bility that the signal is in state a(- 1 -~z(t 0 + 1); rl(to)
= r(t 0 Wa = s 1(t0 ) + n,(,t0 ) [r(t (11) S(to ) + n(to signal as the
input of filter); t = t(a + 0) - dimensionless time; ~z = a/(a + P)
- probability of s4nal being in state -a; P P/(a 4- probabi-
lity of signal being In state +a (signal); Q N(a + 01/U - the
generalized noise to signal ratio. Using the above notation, for a
non-linear system of filtering, the number of false signals per
unit time is derived as
4- 2 2
Y e (10)
n K OA_V~(Q
2 '~
w%ere k is a factor 1im!-,-_'ng the value of noise. For lirear filter-
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S110ci /'6-',,/006/"C)0 9/003 /0 18
Certain optimum instal.-'La,---~ns ... D2--.-L/D302
ing A nxp A k 2 ('2)
Y + ~) - (b +
B A - I A)
B2
and D, (T) ~_A AT + c- A-r
B- Q AQ
Fx(~
are derived for the same where b. b/a. A and B are gi-
ven by
V, -+Kv
A B
D(T) is the probabiliy of nori-detection of a positive pulse, I is
~ot defined. It is-ol,..cjwn chat the theoretical evaluation of filter-
ing errors shows gcod agreement with experimetital resullos of N.K.
Kullman and P.S. Landa (Ref. 6: Radiotekhni-'-a i eiektronika, 1961,
6, 4, 506). From Lhe ob'~aln,~d fcT-mulae for f-J11tering errors -th,?
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2,~520
S/10 61/006/009/003/018
Certain optimum installations D201YI)302
graphs are given which show the properties of signal detection for
a non-linear and a linear filtering system. There are 2 figures and
9 referencest 8 Soviet-bloc and 1 non- Soviet-bloc. The reference
to the English-lasguage publication reads as followet N. Wiener,
Th.e extrapliation, interpolation and smoothing of stationary time
series, J. Wiley, N.Y., 1949.
ASSOCIATION: Fizicheskiy fakulltet moskovskogo gosudarstvennogo
universiteta im. M.V. Lomonosova (Moscow State Univer-
sity im. hT.V. Lomonosovo Paculty of Physics)
SUBMITTED: October 26p 1960
L'9
Card 5/5

STRATONOVICH, R.L. (Mookim)
optimum filtration of a telegraph signal. Avtom. i telem.
22 no.9-1163-1174 S 161. (MIRA 14:9)
(Telegraph) (Information theory)

9c,)5
S/020/61/140/004/004/02"
4 0 (10 3 // /9.7 34Lzt) C111/C444
AUTHOR: Stratonovi ch R. L.
TITLE: Markov's conditional processes in the problems of
mathematical statistics and dynamic programming
PERIODICAL. Akademiya nauk SSSR. Doklady, v. 140, no. 1;, 1961,
769 - 772
TEXT: Let T = i tk : k = 0,1,2 .... t k - t):-i ='N' to = 0.
At, every moment t 9 T a checking decision u t E U t may be made, the
choice of -which depends on the immediately preceeding decision ut-,
such that U 6 U (11 = Ut(ut_,,), where u a = [u, : a,