Croucher Toshio, Bedkihal Salil, Vaccaro Joan A
Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia.
Phys Rev Lett. 2017 Feb 10;118(6):060602. doi: 10.1103/PhysRevLett.118.060602. Epub 2017 Feb 9.
According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.
根据兰道尔原理，擦除一位信息会产生最小的能量消耗。最近，瓦卡罗和巴尼特（VB）在广义吉布斯系综的背景下探讨了信息擦除，并证明对于能量简并的自旋库，擦除成本可以仅用最小量的自旋角动量来衡量，而无需能量。与兰道尔的情况不同，这种情况下的擦除成本与一个本质上离散的自由度相关。在这里，我们研究这种成本中的离散涨落以及违反VB界限的概率。我们还为VB擦除协议得到了一个类似雅尔津斯基等式的式子。我们发现，低于VB界限的涨落比VB擦除的等效雅尔津斯基表达式被指数抑制的速率要大得多且更紧密。我们揭示了涨落大小与擦除成本之间的权衡。我们发现，在库自旋最大极化的 regime 中，涨落的离散性质很明显。我们还阐述了对应于该特定擦除协议中自旋角动量守恒的热力学第一定律。我们的工作对于基于不产生能量成本的信息擦除方案的新型热机将具有重要意义。
