Zhen Yi-Zheng, Egloff Dario, Modi Kavan, Dahlsten Oscar
Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
Phys Rev Lett. 2021 Nov 5;127(19):190602. doi: 10.1103/PhysRevLett.127.190602.
We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit in the framework of stochastic processes. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance.
我们考虑比特重置的能量成本如何随协议的持续时间而变化。比特重置必然在有限时间内发生，在此期间，除了兰道尔推导的准静态功成本之外，还存在额外的代价。这种额外的能量在计算机中以热量形式耗散，从而对不可逆计算机的速度产生了一个基本限制。我们在随机过程的框架内，针对这一限制制定了一个与硬件无关的表达式。我们推导出了功惩罚的封闭形式下限，它是协议执行时间和比特重置误差的函数。该下限适用于离散系统和连续系统，前提仅为主方程满足细致平衡。
