A Thermodynamic Interpretation of Time for Rolling Tachyons

TL;DR

This paper proposes a thermodynamic framework for understanding the evolution of rolling tachyons, relating string theory decay processes to a grand canonical ensemble, and suggests a thermodynamic origin of the arrow of time.

Contribution

It introduces a novel thermodynamic interpretation of time in string theory, connecting brane decay to equilibrium states of a Dyson gas and exploring emergent time concepts.

Findings

Time evolution corresponds to changes in chemical potential and particle number.

Free energy decreases as the system evolves, indicating a thermodynamic arrow of time.

Differential equations relate thermal expectation values at different equilibrium points.

Abstract

We show that the open string worldsheet description of brane decay (discussing a specific example of a rolling tachyon background) can be related to a sequence of points of thermodynamic equilibrium of a grand canonical ensemble of point charges on a circle, the Dyson gas. Subsequent instants of time are related to neighboring values of the chemical potential or the average particle number <N>. The free energy of the system decreases in the direction of larger <N> or later times, thus defining a thermodynamic arrow of time. Time evolution equations are mapped to differential equations relating thermal expectation values of certain observables at different points of thermal equilibrium. This suggests some lessons concerning emergence of time from an underlying microscopic structure in which the concept of time is absent.