Sep 24 – 28, 2023
Faculty of Physics, Astronomy and Applied Computer Science; Jagiellonian University
Europe/Warsaw timezone
Lectures will take place in A1-03 hall (see

Thermodynamically consistent modeling of fuel-driven active engines: effects of the self-propulsion parity

Sep 26, 2023, 4:48 PM
Faculty of Physics, Astronomy and Applied Computer Science; Jagiellonian University

Faculty of Physics, Astronomy and Applied Computer Science; Jagiellonian University

Lojasiewicza 11 30-348 Kraków Poland


Yongjae Oh (Seoul National University)


Engines powered by active particles are well-known for their exceptionally high performance: their efficiency can surpass the Carnot efficiency while simultaneously achieving positive power. However, this 'super-Carnot' behavior arises from considering the apparent statistical signature of the system as a whole, without distinguishing heat and work.

Consequently, this ‘apparent’ description of active heat engines cannot explain how their performances are eventually limited by thermodynamics. To address this issues, thermodynamically consistent theories of active heat engines should be developed.

In this paper, we first develop a theoretical framework which enforces the (anti-)symmetric structure of coupling coefficients between variables so that the system is guaranteed to reach thermodynamic equilibrium in the absence of external driving. Next, we consider a mechano-chemical coupling between a colloidal particle's positional coordinate and a constant chemical driving. This maintains the particle far from equilibrium, resembling the dynamics of the AOUP which is a renowned model of active particle. Additionally, the dynamics of fuel consumption is decided based on the constrained structure of coupling.

Meanwhile, a controversy regarding the thermodynamics of active matter is the behavior of the self-propulsion forces under time reversal. Some literature assume that the sign of self-propulsion force remains unchanged under time-reversal (even-parity), while others assume it changes (odd-parity). Depending on these parity interpretations, two distinct formulas of ‘active work’ (the energy supplied to the particle) are reported.

Using our general framework, we first show that both formulas can be nontrivially recovered under the assumption of tight mechanochemical coupling. This top-down argument demonstrates that that both formulas are possible depending on the specific mechanism of self-propulsion. In addition, we report that the Clausius relation precisely holds between the heat dissipation of the AOUP identified from the first law of thermodynamics, and the entropy production (EP) defined from the path probabilities using the standard tool of stochastic thermodynamics.

Next, we construct an active heat engine with this chemically driven AOUP. From the Clausius relation above, we define a novel concept of efficiency for this engine, which contains both heat injection and chemical fuel consumption in the denominator. This new efficiency is properly bounded from above by the second law of thermodynamics. Also, we can recover the previously reported ‘apparent’ efficiency, providing a clear energetic picture for its super-Carnot behavior.

Another major advantage of this efficiency is that we can address the self-propulsion parity. The efficiency at maximum power (EMP) exhibits a surprisingly simple criterion: the even-parity (odd-parity) engine's EMP is better when the size of the engine is smaller (larger) than the persistence length of the active particle. Also, the EMP depends nonmonotonically on the strength of chemical driving, allowing the EMP of active case being larger than the passive case although the large fuel consumption is properly considered. We finally discuss the existence of a tighter upper bound on the efficiency of the odd-parity engines stemming from the detailed structure of the EP.

[1] Yongjae Oh and Yongjoo Baek, Physical Review E 108, 024602 (2023).

Primary author

Yongjae Oh (Seoul National University)


Prof. Yongjoo Baek (Seoul National University)

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