Highlights

Abstract

Keywords

۱٫ Introduction

۲٫ The five problems of irreversibility

۳٫ Dynamical density functional theory

۴٫ First problem: The source of irreversibility in thermodynamics

۵٫ Second Problem: The Definition of “Equilibrium” and “Entropy”

۶٫ Third problem: The justification of coarse-graining

۷٫ Fourth problem: The (irreversible) approach to equilibrium

۸٫ Fifth problem: The arrow of time

۹٫ Conclusion

Declaration of Competing Interest

Acknowledgments

References

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.

۱٫ Introduction

The temporal asymmetry of thermodynamics is one of the central problems in philosophy of physics. If a cup of hot coffee stands in a room, it will cool down until it has room temperature, but it will not spontaneously heat up by extracting heat from its environment. This is commonly seen as a consequence of the second law of thermodynamics, which assigns to each of these systems a quantity known as “entropy” that increases in these processes and that, most importantly, cannot decrease. Often, this is considered one of the most fundamental laws of physics (Callender, 2001, p. 540).

However, as is also well-known, there is a conflict with the microscopic laws governing the motion of the individual particles that a macroscopic system consists of. These laws are invariant under timereversal,1 which means that if a process can occur in one direction of time, it can also occur in the other direction. Thus, a cup of coffee at room temperature that spontaneously heats up would be in perfect agreement with the microscopic laws of physics, which makes it very difficult to explain why such a behavior is never observed.

An intense discussion on this problem has emerged in philosophy of physics. It has evolved into a variety of sub-debates concerned with different explananda that, in this article will be classified into five problems. Often, foundational discussions of statistical mechanics focus on historical aspects. Moreover, there has been a growth of interest in formal approaches to coarse-graining based on the projection operator formalism (Mori, 1965; Zwanzig, 1960). There is, however, a lack of work that considers the implications of modern research on nonequilibrium statistical mechanics for foundational problems (Wallace, 2015).