Optimal reversible flipping strategies for kinetic Ising models

There is a deep connection between thermodynamics, information and work extraction. Ever since the birth of thermodynamics, various types of Maxwell demons have been introduced in order to deepen our understanding of the second law. Thanks to them it has been shown that there is a deep connection between thermodynamics and information, and between information and work in a thermal system, which usually helps in resolving apparent paradoxes arising when demons are present. Here we show that even in a complex system such as an Ising model, a being with perfect information but satisfying the laws of thermodynamics can extract energy by applying optimal (but local) strategies of spin flipping. We call these entities, in contrast to Maxwell’s demons which have physical superpowers, thermodynamic kobolds. Fig. 1: Representation of the game: the kobolds (a minor demon) observes the phase space of the Ising model and decides to attempt to flip a spin according to an optimal strategy in order to gain energy, attempting to locally lower the energy. However, detailed balance is enforced, and the spin flip can be rejected by the requirement of time reversibility. Introduction. – In later years there has been a lot of interest in the connection between thermodynamics, information and the role that thought experiments involving beings such as Maxwell demons play [1–6]. An example of a Maxwell demon [7] in a thermodynamic system is a being able to observe the speed of particles approaching a gate separating two gases, and open it if only the particle speed is such that the temperature of one of the gases can be raised, or acts in order for the pressure of one can be raised (temperature vs pressure demons). These thought experiments are useful to understand if the second law of thermodynamics can be locally violated. This line of thought has led later many researchers to actually propose various versions of the Maxwell demon, including notoriously Szilard [8,9], Brillouin [10], Landauer [11] and Bennett [12]. A typical Maxwell demon is able, quintessentially but with some restriction depending on the demon, to do anything on the system. Depending on the point of view one takes, these thought experiments often can say something both about the system and the demon itself: if one assumes that thermodynamics is valid, then one can uses these arguments to infer what demons cannot do [13]. On the other hand, if one assumes that the ability of the demons are valid, how thermodynamics can be violated. Either way, these thought experiments present a valid challenge for physicists, forcing them to think carefully about the nature of thermodynamic laws. As in the case of Landauer, and later Bekenstein and Hawking [14–16], can lead to new discoveries about extreme regimes, ranging from nanoscale devices to black holes. A resolution of the violation of the second law can be obtained by assigning information to molecules or atoms, and introducing logical irreversibility on the operation of the operation performed by the demon, leading to an entropy increase due to information erasure. If however no information is erased and the operation is reversible, the second law is not violated. In fact, physical implementations of a Maxwell demon’s have been proposed [17] and realized [18], confirming such picture. These ideas can also be extended from the classical to the quantum realm, p-1 ar X iv :2 20 1. 02 08 1v 1 [ co nd -m at . s ta tm ec h] 6 J an 2 02 2