Editing T-symmetry (section)

====Example: Magnetic Field and Onsager reciprocal relations====
Let us consider the example of a system of charged particles subject to a constant external magnetic field: in this case the canonical time reversal operation that reverses the velocities and the time <math>t</math> and keeps the coordinates untouched is no more a symmetry for the system. Under this consideration, it seems that only Onsager–Casimir reciprocal relations could hold;<ref>{{cite journal |last1=Kubo |first1=Ryogo |title=Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems |journal=Journal of the Physical Society of Japan |date=15 June 1957 |volume=12 |issue=6 |pages=570–586 |doi=10.1143/JPSJ.12.570|bibcode=1957JPSJ...12..570K }}</ref> these equalities relate two different systems, one subject to <math>\vec B</math> and another to <math>-\vec B</math>, and so their utility is limited. However, it was proved that it is possible to find other time reversal operations which preserve the dynamics and so Onsager reciprocal relations;<ref>{{cite journal |last1=Bonella |first1=Sara |last2=Ciccotti |first2=Giovanni |last3=Rondoni |first3=Lamberto |title=Time reversal symmetry in time-dependent correlation functions for systems in a constant magnetic field |journal=EPL (Europhysics Letters) |date=2015 |volume=108 |issue=6 |page=60004 |doi=10.1209/0295-5075/108/60004|s2cid=121427119 }}</ref><ref>{{cite journal |last1=Luo |first1=Rongxiang |last2=Benenti |first2=Giuliano |last3=Casati |first3=Giulio |last4=Wang |first4=Jiao |title=Onsager reciprocal relations with broken time-reversal symmetry |journal=Physical Review Research |date=2020 |volume=2 |issue=2 |page=022009 |doi=10.1103/PhysRevResearch.2.022009|bibcode=2020PhRvR...2b2009L |doi-access=free }}</ref><ref>{{cite journal |last1=Carbone |first1=Davide |last2=Rondoni |first2=Lamberto |title=Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields |journal=Symmetry |date=2020 |volume=12 |issue=8 |pages=1336 |doi=10.3390/sym12081336|arxiv=2008.05193 |bibcode=2020Symm...12.1336C |doi-access=free }}</ref> in conclusion, one cannot state that the presence of a magnetic field always breaks T-symmetry.