Are there thermodynamic cycles on the microscopic scale
Year: 2017
Type: preprint
Abstract: In a previous preprint I proposed to study the thermodynamic cost of computation and control using 'physically universal' cellular automata or Hamiltonians. I defined them as systems that admit the implementation of any desired transformation on a finite target region by first initializing the state of the surrounding and then letting the system evolve according to its autonomous dynamics. This way, one obtains a model of control where each region can play both roles the controller or the system to be controlled. In physically universal systems every degree of freedom is indirectly accessible by operating on the remaining degrees of freedom. In a nutshell, the thermodynamic cost of an operation is then given by the size of the region around the target region that needs to be initialized. In the meantime, physically universal CAs have been constructed by Schaeffer (in two dimensions) and Salo & Torma (in one dimension). Here I show that in Schaeffer's CA the cost for implementing n operations grows linear in n, while operating in a thermodynamic cycle required sublinear growth in order to ensure zero cost per operation in the limit n to infinity. Whether this is a property of every physically universal CA has to be left to future research. After all, physical universality implies a certain kind of instability of information, which could result in lower bounds on the cost of protecting information from its noisy environment.
The technical results of the paper are sparse and quite simple. The contribution of the paper is mainly conceptual and consists in illustrating the type of thermodynamic questions raised by models of control that rely on the concept of physical universality.
Source: arXiv (Cornell University)
Author: Dominik Janzing
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2578910087