Entropic quantum machine

We study nanomachines whose relevant (effective) degrees of freedom $f\gg 1$ but smaller than $f$ of proteins. In these machines, both the entropic and the quantum effects over the whole system play the essential roles in producing nontrivial functions. We therefore call them entropic quantum machines (EQMs). We propose a systematic protocol for designing the EQMs, which enables a rough sketch, accurate design of equilibrium states, and accurate estimate of response time. As an illustration, we design a novel EQM, which shows two characteristic shapes. One can switch from one shape to the other by changing temperature or by applying a pulsed external field. We discuss two potential applications of this example of an EQM.

Figure 1

(a) Proposed EQM. The dots and the line segments represent the sites and the bonds of the lattice, respectively. When an external field is applied, it is applied on the purple area. (b) A part of the EQM. (c) Particle distribution as a function of temperature, $T$. The dashed line represents $n_{\mathrm{av}}$. The scale of $T$ is in units of $J$.

Figure 2

Time evolution of (a) external field, (b) $\langle n_i\left(t\right)\rangle$ for the four sites shown in Fig. 1, and (c) ${\sum }_i{\{[\langle n_i\left(t\right)\rangle -\overline{\langle n_i\rangle }]/n_{\mathrm{av}}\}}^2$. The scale of time $t$ is in units of $\hslash /J$.

Figure 3

Particle distribution as a function of $T$ for (a) $V=0$ and (b) $J=0$. The dashed lines represent $n_{\mathrm{av}}$. The scale of $T$ is taken as the same as in Fig. 1.

Figure 4

(a) Left: An agonist binds to the receptor. Middle: At $T=0.1$, agonists are blocked by the EQM on the receptor. Right: At $T\simeq 3.23$, an agonist passes through the EQM and binds to the receptor. (b) The EQM with the catalyst in it. It catalyzes different reactions depending on the temperature.