Diamantini Maria Cristina
NiPS Laboratory, INFN and Dipartimento di Fisica e Geologia, University of Perugia, Via A. Pascoli, I-06100 Perugia, Italy.
Entropy (Basel). 2023 Jun 28;25(7):984. doi: 10.3390/e25070984.
In this review, we establish a relation between information erasure and continuous phase transitions. The order parameter, which characterizes these transitions, measures the order of the systems. It varies between 0, when the system is completely disordered, and 1, when the system is completely ordered. This ordering process can be seen as information erasure by resetting a certain number of bits to a standard value. The thermodynamic entropy in the partially ordered phase is given by the information-theoretic expression for the generalized Landauer bound in terms of error probability. We will demonstrate this for the Hopfield neural network model of associative memory, where the Landauer bound sets a lower limit for the work associated with 'remembering' rather than 'forgetting'. Using the relation between the Landauer bound and continuous phase transition, we will be able to extend the bound to analog computing systems. In the case of the erasure of an analog variable, the entropy production per degree of freedom is given by the logarithm of the configurational volume measured in units of its minimal quantum.
在本综述中，我们建立了信息擦除与连续相变之间的关系。表征这些相变的序参量衡量系统的有序程度。当系统完全无序时，其值为0；当系统完全有序时，其值为1。这种排序过程可视为通过将一定数量的比特重置为标准值来进行信息擦除。部分有序相中的热力学熵由基于错误概率的广义兰道尔界的信息论表达式给出。我们将在联想记忆的霍普菲尔德神经网络模型中证明这一点，其中兰道尔界为与“记忆”而非“遗忘”相关的功设定了下限。利用兰道尔界与连续相变之间的关系，我们将能够把该界限扩展到模拟计算系统。在模拟变量擦除的情况下，每自由度的熵产生由以其最小量子为单位测量的构型体积的对数给出。
