[Paper Review] Is thermodynamics fundamental?

Michael te Vrugt, Paul Needham+1 more|arXiv (Cornell University)|Apr 9, 2022

Advanced Thermodynamics and Statistical Mechanics4 citations

TL;DR

This paper argues that thermodynamics is a fundamental physical theory, not reducible to statistical mechanics, despite widespread philosophical belief to the contrary. Using four case studies—entropic gravity, black hole thermodynamics, finite-system phase transitions, and the Mori-Zwanzig formalism—it demonstrates that thermodynamics resists reduction due to multiple realizability and foundational constraints, and remains robust even in quantum gravity and non-equilibrium contexts.

ABSTRACT

It is a common view in philosophy of physics that thermodynamics is a non-fundamental theory. This is motivated in particular by the fact that thermodynamics is considered to be a paradigmatic example for a theory that can be reduced to another one, namely statistical mechanics. For instance, the statement "temperature is mean molecular kinetic energy" has become a textbook example for a successful reduction, despite the fact that this statement is not correct for a large variety of systems. In this article, we defend the view that thermodynamics is a fundamental theory, a position that we justify based on four case studies from recent physical research. We explain how entropic gravity (1) and black hole thermodynamics (2) can serve as case studies for the multiple realizability problem which blocks the reduction of thermodynamics. Moreover, we discuss the problem of the reducibility of phase transitions and argue that bifurcation theory (3) allows the modelling of "phase transitions" on a thermodynamic level even in finite systems. It is also shown that the derivation of irreversible transport equations in the Mori-Zwanzig formalism (4) does not, despite recent claims to the contrary, constitute a reduction of thermodynamics to quantum mechanics. Finally, we briefly discuss some arguments against the fundamentality of thermodynamics that are not based on reduction.

Motivation & Objective

• To challenge the widely held philosophical view that thermodynamics is non-fundamental due to its supposed reducibility to statistical mechanics.
• To address the multiple realizability problem in thermodynamics, showing that macroscopic thermodynamic properties like temperature are realized in diverse ways across systems.
• To examine whether recent derivations in quantum foundations (e.g., Mori-Zwanzig formalism) genuinely reduce thermodynamics to quantum mechanics.
• To defend thermodynamics as applicable and fundamental even in extreme physical regimes—such as black holes and quantum gravity—where microscopic theories are incomplete.
• To argue that thermodynamics remains a viable and foundational framework despite exceptions like spin echo experiments, which are rare and context-specific.

Proposed method

• Analyzing entropic gravity and black hole thermodynamics as cases where thermodynamic laws emerge from non-traditional microscopic bases, illustrating multiple realizability.
• Examining spatially resolved thermodynamics and phase field crystal models to show that phase transitions can be described thermodynamically without requiring the thermodynamic limit.
• Evaluating the Mori-Zwanzig formalism for deriving irreversible transport equations, identifying that auxiliary assumptions (e.g., initial conditions) are not derived from quantum mechanics but are instead physically motivated.
• Applying the concept of multiple realizability to show that thermodynamic concepts like temperature and entropy are not uniquely tied to molecular kinetic energy.
• Engaging with counterarguments about non-equilibrium systems and entropy decrease (e.g., spin echo), arguing that such cases are exceptional and do not undermine thermodynamics’ general applicability.
• Using recent advances in thermodynamic modeling (e.g., Thiele et al., 2019) to demonstrate that finite systems can exhibit thermodynamic behavior without infinite idealizations.

Experimental results

Research questions

• RQ1 Can thermodynamics be reduced to statistical mechanics given the problem of multiple realizability?
• RQ2 To what extent do entropic gravity and black hole thermodynamics challenge the reducibility of thermodynamics?
• RQ3 Can phase transitions be described using thermodynamics in finite systems, without relying on the thermodynamic limit?
• RQ4 Does the derivation of irreversible transport equations in the Mori-Zwanzig formalism constitute a genuine reduction of thermodynamics to quantum mechanics?
• RQ5 Are exceptions like the spin echo experiment sufficient to exclude thermodynamics from being a fundamental theory?

Key findings

• Thermodynamics cannot be reduced to statistical mechanics due to the multiple realizability of its core concepts, such as temperature, which are realized in vastly different microscopic ways across systems.
• Black hole thermodynamics and entropic gravity provide strong cases where thermodynamic laws hold without a clear underlying statistical mechanical derivation, suggesting thermodynamics is more fundamental than previously thought.
• Recent developments in phase field modeling allow for thermodynamic descriptions of phase transitions in finite systems, bypassing the need for the thermodynamic limit.
• The derivation of irreversible transport equations in the Mori-Zwanzig formalism relies on auxiliary assumptions (e.g., initial conditions) that are not derived from quantum mechanics but are instead physically motivated, undermining claims of reduction.
• Exceptions to the second law, such as the spin echo experiment, are rare and occur only under highly controlled conditions, and thus do not invalidate thermodynamics as a fundamental theory.
• Thermodynamics remains applicable and reliable in regimes where quantum field theory and general relativity break down, such as in quantum gravity and cosmology, reinforcing its foundational status.