Wormholes and the Thermodynamic Arrow of Time

TL;DR

This paper explores how wormholes in a gravity dual model can influence the thermodynamic arrow of time, showing that entanglement and wormhole-related heat flow can potentially reverse the usual direction of heat transfer, but thermal diffusion dominates.

Contribution

It introduces a model combining entangled states and wormholes to analyze their effects on the thermodynamic arrow of time, revealing the dominance of thermal diffusion over anomalous heat flow.

Findings

Thermal diffusion obeys the thermodynamic arrow of time.

Wormhole-related heat flow can reverse the arrow temporarily.

Thermal diffusion ultimately dominates, preserving the usual thermodynamic direction.

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.