On the logical complexity of tiny heat engines -- and whether they can really be reversible

          @misc{ pirsa_PIRSA:11030123,
            doi = {10.48660/11030123},
            url = {https://pirsa.org/11030123},
            author = {Janzing, Dominik},
            keywords = {Quantum Foundations},
            language = {en},
            title = {On the logical complexity of tiny heat engines -- and whether they can really be reversible },
            publisher = {Perimeter Institute},
            year = {2011},
            month = {mar},
            note = {PIRSA:11030123 see, \url{https://pirsa.org}}
          }
          

Abstract

I consider systems that consist of a few hot and a few cold two-level systems and define heat engines as unitaries that extract energy. These unitaries perform logical operations whose complexity depends on both the desired efficiency and the temperature quotient. I show cases where the optimal heat engine solves a hard computational task (e.g. an NP-hard problem) [2]. Heat engines can also drive refrigerators and use the temperature difference between two systems for cooling a third one. I argue that these triples of systems define a classification of thermodynamic resources [1]. All the above assumes that unitaries are implemented by an external controller. To get a thermodynamically reversible process, the joint process on system and controller must be reversible. Then, the implementation of the joint process requires a "meta-controller", and so on. To study thermodynamic limits without such an infinite sequence of controllers, I introduce the model of "physically universal cellular automata", in which the boundary between system and controller can be shifted (in analogy to the Heisenberg-cut for the quantum measurement problem). I show that this model raises a lot of fundamental questions [3]. Literature: [1] Janzing et al: Thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the second law, J. Stat. Phys. 2000 [2] Janzing: On the computation power of molecular heat engines, J. Stat. Phys. 2006 [3] Janzing: Is there a physically universal cellular automaton or Hamiltonian? arXiv:1009.1720