Page 31 - 2020SEP30 Brief Booklet C

ON THE DECREASE OF ENTROPY 307

tioii of the measurement. Therefore the fol- not possible. But we can try to describe sini-
lowing unequality must be valid : ple nonliving devices that effect such cou-
S+SlO pling, and see if indeed entropy is generated
and in what quantity. Having already recog-
WlSl -I- WZS‘B (12) nized that the only important factor is a
certain characteristic type of coupling, a
+ k(w, log w1 + w2 log WB) 2 0 “measurement,” we need not construct any
This equation must be valid for any values complicated models which imitate the inter-
of w1 and w2 ,3 and of course the constraint vention of living beings in detail. We can be
w2 + wz = 1 cannot be violated. We ask, in satisfied with t,he construction of this par-
particular, for which w1 and w2 and given ticular type of coupling which is accoin-
8-values the expression becomes a minimum. panied by memory.
For the two minimizing values w1 and wz the In our next example, the position co-or-
inequality (12) must still be valid. Under the dinate of an oscillating pointer is “measured”
above constraint, the minimum occurs when by the energy content of a body K. The
the following equation holds : pointer is supposed to connect, in a purely
mechanical way, the body K-by whose
energy content the position of the pointer is
to be measured--by heat conduction with
one of two intermediate pieces, A or B. The
body is connected with A as long as the co-
ordinate-which determines the position of
the pointer-falls into a certain preassigned,
This is easily seen if one introduces the no- but otherwise arbitrarily large or small inter-
tation val a, and ot,herwise if the co-ordinate is in
81 SZ the interval b, with B. Up to a certain mo-
- + log w1 = - + log ~2 = X; (15) ment, namely the moment of the “measure-
k k
ment,” both intermediate pieces will be
then : thermally connected with a heat reservoir at
A
w1 = e .e -Silk ; w2 = eA.e--s2’k. (16) temperature To. At this moment the inser-
tion A will be cooled reversibly to the tem-
If one substitutes these values into the in- perature TA , e.g., by a periodically function-
equality (12) one gets: ing mechanical device. That is, after
e-Sl’k + e--szik ) 20. successive contacts with heat reservoirs of
(17)
intermediate temperatures, A will be brought
Therefore the following also holds: into contact with a heat reservoir of the
temperature Ta . At the same time the inser-
X 2 0. (18)
tion B will be heated in the same way to
If one puts the values w1 and wz from (16) temperature Tg . Then the intermediate
into the equation w1 + w2 = 1, one gets pieces will again be isolated from the corre-
sponding heat reservoirs.
e-S1/k + e--Ss/k - -A (19) We assume that the position of the pointer
- e .
And because X 2 0, the following holds: changes so slowly that all the operations
+ e-‘Zik 5 -. (20) position of the pointer remains unchanged.
e-Sl/k that we have sketched take place while the
1
This equation must be universally valid, if If the position co-ordinate of the pointer fell
thermodynamics is not to be violated. in the preassigned interval, then the body
As long as we allow intelligent beings to was connected with the insertion A during
perforni the intervention, a direct test is the above-mentioned operation, and conse-
quently is now cooled to temperature Ta .
3 The increase in entropy can depend only on In the opposite case, the body is now
the types of measurement and their results but heated to temperature T, . Its energy con-
not on how many systems of one or the other type
were present. tent becomes-according to the position of