EPJ H Highlight - Deciphering Boltzmann’s response to Loschmidt’s paradox

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Published on 28 February 2022

New analysis offers a clarified translation and detailed commentary of Boltzmann’s original reaction to Loschmidt’s paradox

In 1876, Austrian physicist Josef Loschmidt published his ‘reversibility paradox,’ arguing that the time-symmetric processes demanded by fundamental physics are at odds with the second law of thermodynamics. A few months later, Loschmidt’s friend Ludwig Boltzmann, renowned for his statistical interpretation of thermodynamics, published his reaction to the paradox. However, the convoluted nature of his response has long remained baffling to modern readers. Through new analysis published in EPJ H, Olivier Darrigol at the CNRS in France clarifies Boltzmann’s main points, through a new translation and detailed commentary of his 1877 text.

Time-reversal symmetry is a central concept in fundamental physics: describing processes which look the same, regardless of whether time flows forwards or backwards. At the same time, entropy is an inherent physical property of isolated thermodynamic systems, and must always increase as time flows forwards: an idea expressed by the second law of thermodynamics. In his paradox, Loschmidt argued that the stark differences between these two ideas suggested that the second law of thermodynamics cannot be a general theory.

Boltzmann’s reply to his friend’s ideas contained the essential principles of his statistical interpretation of thermodynamics. Compared with his later texts, however, his response is widely seen as difficult to interpret: for reasons including his lack of precise terminology for basic concepts; his mixing of personal intuition with established theories; and his sometimes convoluted writing style.

In a new paper, Darrigol recalls the context of Boltzmann’s argument, offers a new translation of his text, and provides a sentence-by-sentence commentary. In addition, he gives a condensed and clarified summary of Boltzmann’s main points, and offers a criticism of the work – inspired by Boltzmann’s later ideas on the topic, expressed decades later in the 1890s. Ultimately, the new text aims to make Boltzmann’s text understandable to a variety of readers, and to provide fresh insights into his early interpretations of statistical thermodynamics.