E. Schrödinger's 1931 paper "On the Reversal of the Laws of Nature" ["Über die Umkehrung der Naturgesetze",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]

Abstract

We present an English translation of Erwin Schrödinger's paper on "On the Reversal of the Laws of Nature". In this paper Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger's paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of "Euclidean Quantum Mechanics" as probabilistic analogue of quantization. In the second part of the paper Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger's intuitions for contemporary developments in statistical nano-physics.

arXiv commentRevised version. 24 pages, 2 figures. Introduction 2 pages, Translation of the german original pag. 3-10, Commentary pag 10-22

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• (Nonequilibrium) dynamics of diffusion processes with non-conservative drifts
• Two Types of Temporal Symmetry in the Laws of Nature
• Time-reversed Stochastic Inflation
• On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
• Conditioning the tanh-drift process on first-passage times: Exact drifts, bridges, and process equivalences
• Conditioning two diffusion processes with respect to their first-encounter properties
• Torsion-Driven Nonlinearity in Spinless Quantum Mechanics