The Arrow of Time and Its Irreversibility

Stergios Pellis

Mario Castagnino, Manuel Gadella, Olímpia Lombardi

Xi Ming, Qing-yu Cai

This work investigates the fundamental connection between quantum mechanics and thermodynamics through the concept of the arrow of time. While the second law of thermodynamics identifies the arrow of time with the monotonic increase of entropy in isolated systems, closed quantum systems evolve unitarily and conserve von Neumann entropy, making the origin of irreversibility less apparent. Here we establish a no-go theorem proving that correlations in unknown states of closed quantum systems cannot be universally removed by any physical operation. This result demonstrates that correlation generation is inherently irreversible, providing a microscopic and universal basis for the arrow of time. In thermodynamic settings, this irreversibility ensures that heat flows spontaneously from hotter to colder subsystems, reproducing the Clausius formulation of the second law. More generally, the irreversible growth of correlations explains entropy increase, the approach to equilibrium, and decoherence as observable manifestations of the same principle. Our findings ground a quantum-mechanical foundation for the second law of thermodynamics and demonstrate the universality of the arrow of time.

Arno Böhm, Ioannis E. Antoniou, Piotr Kielanowski

The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in-state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.

H. Dieter Zeh

H. D. Zeh