[Paper Review] Thermodynamic implications of non-reciprocity

Sarah A. M. Loos, Sabine H. L. Klapp|arXiv (Cornell University)|Aug 3, 2020

Advanced Thermodynamics and Statistical Mechanics78 references4 citations

TL;DR

This paper demonstrates that non-reciprocal interactions between stochastic degrees of freedom in continuous time and space inherently induce a steady energy flow, driving systems out of equilibrium. It shows that even a single non-reciprocally coupled degree of freedom can extract work from a single heat bath, functioning as a minimal autonomous Maxwell demon, while generating non-Markovian dynamics with complex memory and nonzero information flow.

ABSTRACT

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous Maxwell demon. At the same time, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the flucuating trajectories, without global particle transport.

Motivation & Objective

• To investigate the thermodynamic consequences of non-reciprocal interactions in time- and space-continuous stochastic systems.
• To understand how non-reciprocal coupling leads to steady energy flow and departure from equilibrium.
• To explore the emergence of non-Markovian dynamics and information flow when non-reciprocally coupled variables are projected out.
• To determine whether non-reciprocal systems can extract work from a single heat bath, mimicking a Maxwell demon.
• To characterize the active matter-like behavior of such systems, including positive energy input without net particle transport.

Proposed method

• Analyzing continuous-time, continuous-space stochastic systems with non-reciprocal couplings between degrees of freedom.
• Deriving effective one-variable Langevin equations after projecting out non-reciprocally coupled variables, resulting in non-Markovian dynamics with complex memory kernels.
• Applying a generalized second law of thermodynamics that includes information flow terms in non-Markovian systems.
• Using linear non-reciprocal interactions to engineer non-monotonic memory functions, analogous to time-delayed feedback control.
• Formulating the thermodynamic behavior under isothermal conditions to assess work extraction from a single heat bath.
• Quantifying energy and information fluxes along individual fluctuating trajectories to assess active behavior and non-equilibrium steady states.

Experimental results

Research questions

• RQ1 What thermodynamic effects arise from non-reciprocal coupling in continuous stochastic systems?
• RQ2 Can a single non-reciprocally coupled degree of freedom extract work from a single heat bath under isothermal conditions?
• RQ3 How does projecting out non-reciprocally coupled variables lead to non-Markovian dynamics with complex memory?
• RQ4 What is the role of information flow in non-Markovian systems with non-reciprocal interactions?
• RQ5 How do such systems exhibit active matter-like behavior without global particle transport?

Key findings

• Non-reciprocal coupling alone induces a steady energy flow, implying a non-equilibrium state even in the absence of external driving.
• Projecting out non-reciprocally coupled degrees of freedom results in non-Markovian Langevin equations with complex memory kernels.
• A generalized second law of thermodynamics is derived that includes information flow terms, extending the second law to non-Markovian systems.
• Non-reciprocal linear interactions can generate non-monotonic memory functions, characteristic of time-delayed feedback, and are intrinsically linked to nonzero information flow.
• A single non-reciprocally coupled degree of freedom can extract energy from a single heat bath at isothermal conditions, functioning as a minimal autonomous Maxwell demon.
• The system exhibits positive energy input on individual fluctuating trajectories, consistent with active matter, despite no net particle transport.