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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite In Perspectives on Statistical Thermodynamics, Yoshitsugu Oono, it is written that Do not conclude, however, that since the second law is invincible, information thermodynamics is unimportant. It is possible for a system we are interested in to perform something that ordinary thermodynamics does not allow, and to pay the price somewhere else. For example, it may be possible to go beyond the limit of thermodynamics for the time being by shifting the average value of fluctuations, although the price must be paid (dearly) later. There must be such cases in molecular machines. It is argued that cell senescence is due to the accumulation of defects and wastes, but cell death could have a more active implication of carrying away the debt caused by utilizing information. Thus, entropic apoptosis and entropic altruism are conceivable. but I don't understand the following two points. Why is cell death assoc

Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite 1 $newcommandqr[1]$ I gave myself the task of building an operator that implements the following function: $f(0) = 0$ , $f(1) = 1$ , $f(2) = 1$ , $f(3) = 0$ . I restricted myself to $x$ up to 2 bits. That is, $f$ tells the parity of its argument. I read that in order to be reversible, a circuit $U_f$ could be defined to have the following effect: $U_fqrx_2 qr0_1 to qrx_2qr0 oplus f(x)_1$ . After doing my calculations, I think the following matrix represents $U_f$ $$beginbmatrix 1 & 0 & 0 & 0\ 0 & 1 & 1 & 0\ 0 & 0 & 0 & 0\ 0 & 0 & 0 & 0 endbmatrix otimes I_2$$ However, I'm really not sure. I once read that this definition isn't complete, that I should also define the behavior for the input $qrx_2qr1$ . (I'm not too clear on that.) So --- though confused ---, I went ahead and defined $$U_fqrx_2 qr1_1 to qrx_2qr1 oplus f(x)_1.$$ Doing my calculations ag