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Second law-abiding-account of heat engines in active bath

Yi-Hung Liao (廖宜鴻)1, Jerard Vincent Ang1, Pik-Yin Lai (黎璧賢)1,2,*, and Yonggun Jun (전용근)1,†

  • *Contact author: pylai@phy.ncu.edu.tw
  • †Contact author: yonggun@phy.ncu.edu.tw
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Phys. Rev. Research 8, 023136 – Published 8 May, 2026

DOI: https://doi.org/10.1103/2yzz-mq4r

Abstract

The second law of thermodynamics, quantitatively formalized through non-negative entropy production, defines the fundamental constraints on energy conversion, such as the Carnot limit for heat engines. While it has been suggested that active noises in heat baths might allow microscopic engines to surpass these bounds, such apparent violations often stem from an incomplete thermodynamic accounting of the active reservoir. Here, we demonstrate theoretically and experimentally that the classical second law remains valid when considering active noise as a particle under white Gaussian noise interacting with a Brownian bead, rather than relying on the concept of effective temperature. In this study, our illustrative model system consists of a two-dimensional Brownian gyrator with a bead immersed in temperature baths, combined with active noises. By treating active noise as explicit degrees of freedom, we analytically solve the Langevin equation by decoupling the energetics into two contributions: the interactions of the Brownian bead with the heat baths and with another particle subject to a different heat bath. We find that entropy production is always non-negative; the gyrator can operate as a heat engine in specific environments but cannot surpass the Carnot limit, and the thermodynamic uncertainty relation holds. This study offers a rigorous perspective on the relation between active noise and the second law, demonstrating that properly accounting for active noise as a distinct thermodynamic component preserves the fundamental principles of thermodynamics.

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Phys. Rev. Research 8, 023136– Published 8 May, 2026
  • Received 2 December 2025
  • Accepted 18 April 2026
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