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[ACG32-P17] The Boundary Current Synchronization Is a Maxwell's Demon
Keywords:Phase Synchronization, Kuroshio Current, Gulf Stream, Information Thermodynamics, Nonequilibrium Physics
It is crucial for climate dynamics to understand the variability of the western boundary currents on interannual to decadal time scales. Kohyama et al. [1] discovered synchronization in the sea surface temperatures (SSTs) of the Gulf Stream and the Kuroshio Current, namely the Boundary Current Synchronization (BCS). They argued for the necessity of mid-latitude interbasin coupling mediated by the atmosphere (i.e., information transmission) for the BCS. Meanwhile, over the last two decades, the fusion of information theory with non-equilibrium physics has given birth to information thermodynamics [2]. Using methods from this emerging field, we show the possibility that the BCS can be understood as a Maxwell's demon system and discuss the role of each current in the climate system.
A Maxwell's demon system refers to a system that uses information about its state to rectify fluctuations [2]. For illustration, consider a single particle in an isothermal environment (Fig. 1). This particle fluctuates due to heat from the surroundings. First, the 'demon' inserts a wall into the box and measures the particle position. Next, the 'demon' controls the direction of the wall movement based on the measurement outcome, extracting work through isothermal expansion. The source of this expansion is the thermal fluctuation from the surroundings. Finally, the 'demon' removes the wall and returns the system to its initial state. Since work is extracted in the isothermal cycle, it apparently violates the second law of thermodynamics. In this cycle, feedback control is performed based on the measurement, converting fluctuations into work. By accounting for the amount of information obtained from the measurement, an inequality that extends the conventional second law can be derived [2-5].
Maxwell's demon systems can also be realized in autonomous systems described by differential equations [4, 5]. In this case, depending on the sign of an information flow described below, the total system is divided into a 'demon' (i.e., controller) and a 'particle' (i.e., controlled subsystem).
We consider a bivariate autonomous model for the BCS (Eqs. 1 and 2), which describes the time evolution of the regional mean SSTs of the Gulf Stream (TG) and the Kuroshio (TK). The first term in each equation represents relaxation, the second term represents interaction, and the third term represents white Gaussian noise (fluctuations). All coefficients are positive and were estimated from the time series data [1] of satellite observations and a global climate model. Equations 1 and 2 well reproduce the BCS.
Numerical analysis based on the second law of information thermodynamics [4, 5] shows that the above model is in the parameter regime that satisfies Eqs. 3 and 4. The left quantity in each equation is the rate of entropy change associated with fluctuations. The right quantity is the information flow between the boundary currents and represents the gain or loss of information through interaction.
The negative information flow from the Kuroshio to the Gulf Stream (Eq. 3) is interpreted as the Gulf Stream being a 'particle' that loses information through 'control' (Fig. 2). The associated negative rate of entropy change corresponds to the extracted work. On the other hand, the positive information flow from the Gulf Stream to the Kuroshio (Eq. 4) is interpreted as the Kuroshio being a 'demon' that gains information through 'measurement' (Fig. 2). This result suggests that the BCS can be understood as a Maxwell's demon system that autonomously rectifies fluctuations.
This understanding implies different roles for the boundary currents. The Gulf Stream forces the SST of the Kuroshio to synchronize in phase. In contrast, the Kuroshio does not force the SST of the Gulf Stream but rather tends to fix the phase by suppressing changes in the Gulf Stream. When both currents are coupled in an appropriate parameter regime, synchronization occurs using the fluctuations in the atmosphere and ocean as a driving source.
[1] Kohyama et al., 2021, Science.
[2] Shiraishi, 2023, Springer.
[3] Sagawa and Ueda, 2010, Phys. Rev. Lett.
[4] Horowitz and Esposito, 2014, Phys. Rev. X.
[5] Loos and Klapp, 2020, New J. Phys.
A Maxwell's demon system refers to a system that uses information about its state to rectify fluctuations [2]. For illustration, consider a single particle in an isothermal environment (Fig. 1). This particle fluctuates due to heat from the surroundings. First, the 'demon' inserts a wall into the box and measures the particle position. Next, the 'demon' controls the direction of the wall movement based on the measurement outcome, extracting work through isothermal expansion. The source of this expansion is the thermal fluctuation from the surroundings. Finally, the 'demon' removes the wall and returns the system to its initial state. Since work is extracted in the isothermal cycle, it apparently violates the second law of thermodynamics. In this cycle, feedback control is performed based on the measurement, converting fluctuations into work. By accounting for the amount of information obtained from the measurement, an inequality that extends the conventional second law can be derived [2-5].
Maxwell's demon systems can also be realized in autonomous systems described by differential equations [4, 5]. In this case, depending on the sign of an information flow described below, the total system is divided into a 'demon' (i.e., controller) and a 'particle' (i.e., controlled subsystem).
We consider a bivariate autonomous model for the BCS (Eqs. 1 and 2), which describes the time evolution of the regional mean SSTs of the Gulf Stream (TG) and the Kuroshio (TK). The first term in each equation represents relaxation, the second term represents interaction, and the third term represents white Gaussian noise (fluctuations). All coefficients are positive and were estimated from the time series data [1] of satellite observations and a global climate model. Equations 1 and 2 well reproduce the BCS.
Numerical analysis based on the second law of information thermodynamics [4, 5] shows that the above model is in the parameter regime that satisfies Eqs. 3 and 4. The left quantity in each equation is the rate of entropy change associated with fluctuations. The right quantity is the information flow between the boundary currents and represents the gain or loss of information through interaction.
The negative information flow from the Kuroshio to the Gulf Stream (Eq. 3) is interpreted as the Gulf Stream being a 'particle' that loses information through 'control' (Fig. 2). The associated negative rate of entropy change corresponds to the extracted work. On the other hand, the positive information flow from the Gulf Stream to the Kuroshio (Eq. 4) is interpreted as the Kuroshio being a 'demon' that gains information through 'measurement' (Fig. 2). This result suggests that the BCS can be understood as a Maxwell's demon system that autonomously rectifies fluctuations.
This understanding implies different roles for the boundary currents. The Gulf Stream forces the SST of the Kuroshio to synchronize in phase. In contrast, the Kuroshio does not force the SST of the Gulf Stream but rather tends to fix the phase by suppressing changes in the Gulf Stream. When both currents are coupled in an appropriate parameter regime, synchronization occurs using the fluctuations in the atmosphere and ocean as a driving source.
[1] Kohyama et al., 2021, Science.
[2] Shiraishi, 2023, Springer.
[3] Sagawa and Ueda, 2010, Phys. Rev. Lett.
[4] Horowitz and Esposito, 2014, Phys. Rev. X.
[5] Loos and Klapp, 2020, New J. Phys.