Abstract
In classical thermodynamics, heat cannot spontaneously pass from a colder system to a hotter system, which is called the thermodynamic arrow of time. However, if the initial states are entangled, the direction of the thermodynamic arrow of time may not be guaranteed. Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space. We make the temperature difference between the two sides by changing the Hamiltonian. We turn on proper interaction between the two sides and calculate the changes in energy and entropy. The energy transfer, as well as the thermodynamic arrow of time, are mainly determined by the competition between two channels: thermal diffusion and anomalous heat flow. The former is not related to the wormhole and obeys the thermodynamic arrow of time; the latter is related to the wormhole and reverses the thermodynamic arrow of time, i.e. transferring energy from the colder side to the hotter side at the cost of entanglement consumption. Finally, we find that the thermal diffusion wins the competition, and the whole thermodynamic arrow of time has not been reversed.
Highlights
With the experimental advances in the last two decades, it is possible to prepare and control systems with an increasing number of atoms, whose scale stretches across the gap between macroscopic thermodynamics and microcosmic quantum mechanics
The energy transfer, as well as the thermodynamic arrow of time, are mainly determined by the competition between two channels: thermal diffusion and anomalous heat flow. The former is not related to the wormhole and obeys the thermodynamic arrow of time; the latter is related to the wormhole and reverses the thermodynamic arrow of time, i.e., transferring energy from the colder side to the hotter side at the cost of entanglement consumption
The thermodynamic arrow of time plays a crucial role in the second law of thermodynamics, which refers to the phenomenon that heat will spontaneously pass from a hotter system to a colder system
Summary
With the experimental advances in the last two decades, it is possible to prepare and control systems with an increasing number of atoms, whose scale stretches across the gap between macroscopic thermodynamics and microcosmic quantum mechanics. The AdS/CFT correspondence is a realization of the holography principle, proposed by Susskind according to the surface law of black hole entropy It conjectures that the degree of freedom of a gravitational system can be mapped to its boundary [15]. V, with proper interactions, we find two channels which mainly contribute to the energy transfer: the thermal diffusion via the boundary and the anomalous heat flow via the wormhole in the eternal black hole The former is numerically larger than the latter. We focus on the eternal black hole in the main text, in Appendixes B and C, similar issues are investigated for a product state in JT gravity and a TFD or product state in the Sachdev-Ye-Kitaev (SYK) model for comparison
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