Can the second law be compatible with time reversal invariant dynamics?

• Explicates the tension between the second law and the time reversal invariance of dynamics.
• Shows that the tension does not depend on the version of the second law.
• Disputes Uffink׳s arguments on the time reversal invariance of different versions of the second law.
• Discusses Lieb and Yngvason׳s version of the second law.
• Compares traditional and axiomatic versions of the second law.

It is commonly thought that there is some tension between the second law of thermodynamics and the time reversal invariance of the microdynamics. Recently, however, Jos Uffink has argued that the origin of time reversal non-invariance in thermodynamics is not in the second law. Uffink argues that the relationship between the second law and the time reversal invariance depends on the formulation of the second law. He claims that a recent version of the second law due to Lieb and Yngvason allows irreversible processes, yet is time reversal invariant.In this paper, I attempt to spell out the traditional argument for incompatibility between the second law and the time reversal invariant dynamics, making the assumptions on which it depends explicit. I argue that this argument does not vary with different versions of the second law and can be formulated for Lieb and Yngvason׳s version as for other versions. Uffink׳s argument regarding time reversal invariance in Lieb and Yngvason is based on a certain symmetry of some of their axioms. However, these axioms do not constitute the full expression of the second law in their system.