Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields
arXiv:2008.05193 · doi:10.3390/sym12081336
Abstract
Time reversal invariance (TRI) of particles systems has many consequences, among~which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the~strict traditional notion of reversibility that led to Casimir's work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We~first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.
arXiv comment12 pages
References in corpus (5)
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Relativistic Brownian Motion
- Onsager Relations in Coupled Electric, Thermoelectric and Spin Transport: The Ten-Fold Way
- Exact solutions of the Schrodinger equation with non central potential by Nikiforov Uvarov method
- Maxwell-Juttner distributions in relativistic molecular dynamics
Cited by in corpus (5)
- Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
- Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
- Fluctuation relations for systems in constant magnetic field
- Time Reversal Symmetry for Classical, Nonrelativistic Quantum and Spin Systems in Presence of Magnetic Fields
- Fluctuation relations for dissipative systems in constant external magnetic field: theory and molecular dynamics simulations