Abstract
The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.
Highlights
The total thermodynamic entropy S, in equilibrium, must be Lorentz invariant
Foundations of Physics (2022) 52:11 probabilities, which are supposed to have an invariant nature [10, 11]. When it comes to proving rigorously, from first principles, that the thermodynamic entropy must necessarily be a scalar, some conceptual problems arise and it is easy to fall into circular reasoning
Motivated by the complication outlined in the previous subsection, we need to make an argument for the Lorentz invariance of the entropy which does not build on the assumption that the second law of thermodynamics is valid for every observer
Summary
The total thermodynamic entropy S, in equilibrium, must be Lorentz invariant. Whether we identify S with the Boltzmann entropy [1, 2], or with the Gibbs/Shannon entropy [3, 4], or with the von Neumann entropy [5, 6], its Lorentz invariance seems inescapable. This fact is a foundational feature of relativistic fluid dynamics [7, 8] and of thermal quantum field theory [9]. The invariance of the entropy with respect to Lorentz transformations is usually justified by invoking its statistical connection with microscopic
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