Understanding Time Reversal in Quantum Mechanics: A New Derivation

Mario Castagnino, Manuel Gadella, Olímpia Lombardi

Richard Joseph Oldani

Matrix mechanics is not considered important for understanding quantum mechanics; however, it is the key to understanding time reversal asymmetry. We use a single, solitary atom to derive the diagonalized Hamiltonian matrix in continuous time and use it to visualize the irreversibility of time in a quantum system. Graphic evidence in support of the model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Theoretical arguments supporting time asymmetry in statistical mechanics that were presented by Feynman and Einstein are also cited. It is hypothesized that equations describing time reversal asymmetry must be derived in energy-time coordinates.

Cristian López

Jiří Souček

Quantum Mechanics (QM) is primarily a probabilistic theory. The standard Kolmogorov probability theory is not suitable for this goal since it does not offer the possibility of the reversible time evolution. This implies the need to construct a new probability theory which is able to model the reversible time evolution. I have proposed such an Extended probability theory. The main goal of this project is to understand what QM is. In this note I shall describe the program of the research which is already partially realized.

Woon Siong Gan

Alberto Rolandi

The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and thermodynamics, with a particular focus on minimizing entropy production in finite-time processes. By employing tools from quantum information theory and geometric thermodynamics, we tackle the challenge of deriving irreversible thermodynamic behavior from the reversible microscopic framework of quantum mechanics. We begin with a comprehensive review of the laws of thermodynamics, setting the stage for the subsequent analyses. We introduce novel developments in quantum thermodynamics through a generalized framework for geometric thermodynamics, which enables the derivation of finite-time corrections beyond the Markovian regime. Building on this foundation, we extend Landauer's principle by incorporating a finite-time correction that highlights the necessity of strong coupling for optimal information erasure processes. This result underscores the emergence of Planckian time as a fundamental speed limit to thermalization. Additionally, we explore how collective effects can be harnessed to reduce energy dissipation in thermodynamic operations, revealing that classical correlations between systems can significantly mitigate dissipation, though this may pose new questions regarding the third law of thermodynamics. Finally, we optimize thermodynamic processes in mesoscopic systems, including quantum dot engines and information engines. These findings not only enhance our understanding of the fundamental limits of irreversibility but also open new avenues for research. Future works will focus on fully exploiting collective effects, aligning these with the third law of thermodynamics, and understanding the thermodynamic consistency of master equations.