Conservation Laws and Thermodynamic Efficiencies

We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.

Figure 1

The current-current correlation functions for various system sizes with $\Lambda =256$ (red dashed curve), 512 (blue dash-dotted curve), and 1024 (black solid curve). The temperature $T=1$, particle masses are ${\nu }_1=1$ and ${\nu }_2=\sqrt{5}$. It is seen that all the current-current correlation functions approach a finite nonzero value as the correlation time increases and that the characteristic time scale to approach such value is independent of the system size. Note that in all the figures the particle density is fixed to be $N/\Lambda =1$ and $N_1=N_2=N/2$.

Figure 2

Comparison between the numerically determined finite-size generalized Drude weights (symbols) and their analytical values (lines) given by Eq. (16) for $\Lambda =256$. We set $T=1$ and ${\nu }_1=1$ in (a) and ${\nu }_1=1$, ${\nu }_2=\sqrt{5}$ in (b).

Figure 3

Dependence of the Onsager coefficients $L_{ij}$ on the system size $\Lambda$. The straight lines are the best linear fitting, $L_{ij}\propto \Lambda$. In these nonequilibrium simulations we set the temperature $T=1$, the chemical potential $\mu =0$, and the masses ${\nu }_1=1$ and ${\nu }_2=\sqrt{19}$.

Figure 4

Dependence of the transport coefficients $\sigma$, $S$, $\kappa$, and $ZT$ on the system size $\Lambda$, for the same parameter values as in Fig. 3. Dashed lines are drawn for reference.