Complexity vs energy: theory of computation and theoretical physics

3Quantum: Algebra Geometry Information

物理学;数学

Manin, Y.I.^1

Max-Planck-Institut für Mathematik, Vivatsgasse 7, Bonn

53111, Germany^1

关键词: Geometry information;    Quantum field theory;    Theoretical computer science;    Theoretical physics;    Theory of computation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012018/pdf
DOI  :  10.1088/1742-6596/532/1/012018

来源: IOP

【 摘 要 】

This paper is a survey based upon the talk at the satellite QQQ conference to ECM6, 3Quantum: Algebra Geometry Information, Tallinn, July 2012. It is dedicated to the analogy between the notions of complexity in theoretical computer science and energy in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested recently, in which mathematics related to (un)computability is inspired by and to a degree reproduces formalisms of statistical physics and quantum field theory.