标题： 基于令牌的布朗电路中具有记忆的保守连接及其热力学成本 显示英文标题

标题： Conservative Join with memory in token-based Brownian circuits and its thermodynamic cost

摘要： 基于令牌的布朗电路利用粒子的布朗运动进行计算。 保守联接（CJoin）是一种电路元件，用于同步两个布朗粒子，其实现使用排斥粒子，如磁性斯格明子或电子，对于构建布朗电路至关重要。 在这里，提出了一种使用简单的量子点电路实现CJoin的理论方法，包括一个内部状态——双量子点，它充当一位存储器，存储两粒子转移的方向。 引入了一个周期性重置协议，允许CJoin以特定方向发射粒子。 在周期性重置下的随机热力学识别热力学成本为重置所做的功减去由于重置导致的熵减少，在温度为$T$时，其下限保持在$k_{\rm B} T$的几倍以内。 将速度限制关系应用于双部分动力学中的子系统，表明发射粒子的数量由涉及子系统的不可逆熵产生率和动力学活动率的表达式相对紧密地上界。 显示英文摘要

摘要： The token-based Brownian circuit harnesses the Brownian motion of particles for computation. The conservative join (CJoin) is a circuit element that synchronizes two Brownian particles, and its realization using repelling particles, such as magnetic skyrmions or electrons, is key to building the Brownian circuit. Here, a theoretical implementation of the CJoin using a simple quantum dot circuit is proposed, incorporating an internal state-a double quantum dot that functions as a one-bit memory, storing the direction of two-particle transfer. A periodic reset protocol is introduced, allowing the CJoin to emit particles in a specific direction. The stochastic thermodynamics under periodic resets identifies the thermodynamic cost as the work done for resets minus the entropy reduction due to resets, with its lower bound remaining within a few multiples of $k_{\rm B} T$ at temperature $T$. Applying the speed limit relation to a subsystem in bipartite dynamics, the number of emitted particles is shown to be relatively tightly bounded from above by an expression involving the subsystem's irreversible entropy production rate and dynamical activity rate.