[Paper Review] The Arrow of Time and Correlations in Quantum Physics

Vlatko Vedral|arXiv (Cornell University)|May 3, 2016

Advanced Thermodynamics and Statistical Mechanics6 references3 citations

TL;DR

This paper proposes that the quantum arrow of time arises from the increase of correlations—quantified by von Neumann mutual information—between a system and its environment during unitary evolution. It shows that entropy increase is guaranteed only if there are no initial correlations; otherwise, entropy can decrease, implying that initial correlations are a potential resource for violating the second law.

ABSTRACT

We discuss the arrow of time in terms of the increase of correlations between the system and its environment. Here we show that the existence of the arrow of time, based on deleting correlations, requires a strict absence of initial correlations between the system and the environment. We discuss our work in relation to other approaches addressing the same problem and emphasise similarities and differences.

Motivation & Objective

• To investigate the origin of the arrow of time in quantum physics through the lens of correlations between a system and its environment.
• To determine whether the increase in entropy and irreversibility can be explained by the growth of mutual information under unitary dynamics.
• To assess the role of initial correlations in potentially reversing entropy increase, challenging the universality of the second law.
• To contrast this correlation-based explanation with alternative approaches such as Crooks' fluctuation theorem and the role of thermalization.

Proposed method

• Analyzes a global unitary evolution on a composite system and environment initially uncorrelated: $\rho_{SR} = \rho_S \otimes \rho_R$.
• Computes the change in total entropy as $\Delta S_S + \Delta S_R = I(S':R')$, where $I$ is the von Neumann mutual information in the final state.
• Uses the non-negativity of mutual information to show that entropy increase is equivalent to correlation generation.
• Considers the effect of initial correlations: if $\rho_{SR}$ is not a product state, the entropy change can be negative, implying potential violation of the second law.
• Compares with the Crooks fluctuation theorem, showing that irreversibility there arises from thermalization, not correlation deletion.
• Uses relative entropy between forward and backward probability distributions to quantify entropy increase, distinguishing it from mutual information.

Experimental results

Research questions

• RQ1 Can the arrow of time in quantum physics be explained by the increase of correlations between a system and its environment?
• RQ2 What happens to the second law of thermodynamics if initial correlations between system and environment are non-zero?
• RQ3 How does the correlation-based explanation of irreversibility differ from the fluctuation theorem approach based on thermalization?
• RQ4 Under what conditions can entropy decrease in a unitary quantum evolution, and what does this imply for the second law?
• RQ5 Is the arrow of time fundamentally tied to the deletion of correlations, or is it more accurately linked to initial conditions?

Key findings

• The increase in total entropy during unitary evolution is exactly equal to the final mutual information between system and environment, $I(S':R')$, when the initial state is uncorrelated.
• If initial correlations are present, the entropy change can be negative, meaning the second law can be violated in principle.
• The paper demonstrates that the second law is not universally valid under unitary evolution unless the initial state is uncorrelated.
• The correlation-based explanation of the arrow of time is falsifiable: if future observations show entropy decrease without heat waste, it would support this model.
• The approach differs from Crooks' fluctuation theorem, where irreversibility arises from starting the reverse protocol from the final thermal state, not from correlation deletion.
• Quantum measurements do not explain the arrow of time, as they can be time-symmetrically formulated and do not inherently break time-reversal symmetry.