A third law of thermodynamics is an unnecessary complexity

TL;DR

The paper argues that a separate Third Law of thermodynamics is unnecessary because Planck's universal statement of the Second Law, together with energy conservation, already enforces the boundary behavior at absolute zero. By tracing continuity arguments, ontological consistency, adiabatic processes, and the form of equations of state, the author derives Nernst-type constraints as intrinsic consequences of the Second Law rather than as an independent postulate. This approach reframes the Nernst theorem as a consistency check rather than a new physical discovery, addressing historical debates (e.g., Einstein–Nernst) and emphasizing parsimony in thermodynamic axioms. The work highlights that the Third Law functions as a consistency regulator at the boundary, with potential implications for how thermodynamic foundations are taught and formalized. $T=0$ boundary behavior, entropy accumulation, and the relation between $Q$, $W$, and $\Delta S$ are treated through Planckian logic, illustrating a unified framework across the entire temperature domain.

Abstract

This paper elaborates on the implications of the relationship between the Second and Third Laws and provides a comprehensive formal and historical justification for the logical redundancy of the Nernst heat theorem. By revisiting the Nernst-Einstein debate, the underlying hypotheses that lead to the traditional view of the Third Law as an independent postulate are examined. It is argued that the historical rejection of Nernst's proof -- motivated by Einstein's insistence on the practical non-performability of cycles at absolute zero -- overlooks the fact that a universal Second Law already precludes such cycles, rendering an independent Third Law an unnecessary complexity. Ultimately, the Nernst theorem is shown to be an essential consistency regulator rather than an independent physical discovery.

Figures (2)

• Figure 1: Comparison between observed (A, left) and hypothetical (B, right) thermodynamic behaviors as $T \to 0$.Masanes2017 Panel A shows the standard behavior consistent with the Nernst theorem (Third Law) whicl panel B depicts a substance violating the Nernst theorem. Gray shaded regions indicate inaccessible states within the domain of $x$, a mechanical parameter. In panel A, $abcda$ is a generalized Carnot engine consisting in two isothermal processes and two processes that differ in a constant shift of entropy. The net balance of a generalized Carnot engine is Carnot engine. The temperature $T_c^\star$ is the lowest temperature at which the engine can operate for the given working substance and the given $\Delta S=S_b-S_a$.Martin-Olalla2003b In panel B the cycle $abcda$ is a Carnot engine operating between non-zero temperatures $T_b$ and $T_c$; the cycle $ABCDA$ is a Carnot engine operating at $T=0$.
• Figure 2: Axiomatic map of the macroscopic framework. The diagram illustrates how Planck's statement of the Second Law serves as the foundation for the thermodynamic hierarchy. From it, the ordering of states leads to the definition of absolute temperature $T$ and Clausius entropy $S$ from which Nernst's theorem is proven, see (\ref{['eq:6']}). The convergence of the evolution criterion and stability requirements ($c_y > 0$) towards the $T \to 0$ limit leads to the vanishing of the specific heats. Both lines converge in the statement "the entropy of a chemically homogeneous body with finite density approaches to a definite value as temperature decreases indefinitely".