The Five Problems of Irreversibility

Abstract

Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this "problem of irreversibility" often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considered in philosophy of physics, for this debate. For this purpose, the philosophical discussion of irreversibility is structured into five problems, concerned with the source of irreversibility in thermodynamics, the definition of equilibrium and entropy, the justification of coarse-graining, the approach to equilibrium and the arrow of time. For each of these problems, it is shown that DDFT provides novel insights that are of importance for both physicists and philosophers of physics.

Updated with accepted manuscript

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• Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem
• The Mereology of Thermodynamic Equilibrium
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism
• How to distinguish between indistinguishable particles
• Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility