Thermodynamics from relational imaginary time evolution

Thermodynamics is traditionally described with statistical ensembles in quantum or classical mechanics. Canonical typicality [1] has related thermodynamics for a system to ensembles of global energy eigenstates of system and its environment analyzing their cardinality. We derive thermodynamics from a single, maximally entangled global state extending the concept of relational time [2-4] to complex relational time.

[1] S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical typicality, Phys. Rev. Lett. 96, 050403 (2006).

[2] D. N. Page and W. K. Wootters, Evolution without evolution: Dynamics described by stationary observables, Phys. Rev. D 27, 2886 (1983).

[3] A. R. H. Smith and M. Ahmadi, Quantizing time: Interacting clocks and systems, Quantum 3, 160 (2019).

[4] S. Gemsheim and J. M. Rost, Emergence of time from quantum interaction with the environment, Phys. Rev. Lett. 131, 140202 (2023).