In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics descripti...

Thermodynamics problems for the single-phase-lagging (SPL) model have not been much studied. In this paper, the violation of the second law of thermodynamics by the SPL model is studied from two perspectives, which are the negative entropy production rate and breaking equilibrium spontaneously. The methods for the SPL model to avoid the negative entropy production rate are proposed, which are e...

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise appr...

Extending the analysis in our previous paper, we construct the entanglement thermodynamics for a massless scalar field on the Schwarzschild spacetime. Contrary to the flat case, the entanglement energy Eent turns out to be proportional to area radius of the boundary if it is near the horizon. This peculiar behavior of Eent can be understood by the red-shift effect caused by the curved backgroun...

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to...

In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we establish the ex...

The nonequilibrium thermodynamics framework is tailored in the present paper to formulate the gas/liquid/solid system. In this system, there are two important issues, namely, the contact line motion and contact angle change, and shear stress singularity, during the dynamic evolution. Traditionally, the fluid mechanics approach has been applied to model these two issues. In the present paper, we...

We study the non-critical space-time non-commutative open string (NCOS) theory using a dual supergravity description in terms of a certain near-horizon limit of the F1-Dp bound state. We find the thermodynamics of NCOS theory from supergravity. The thermodynamics is equivalent to Yang-Mills theory on a commutative space-time. We argue that this fact does not have to be in contradiction with the...

We summarize in this article the experiments which have been performed to test the theoretical findings in stochastic thermodynamics such as fluctuation theorem, Jarzynski equality, stochastic entropy, out-ofequilibrium fluctuation dissipation theorem, and the generalized first and second laws. We briefly describe experiments on mechanical oscillators, colloids, biological systems, and electric...

We survey a few aspects of the thermodynamics of computation, connecting information, thermodynamics, computability and physics. We suggest some lines of research into how information theory and computational thermodynamics can help us arrive at a better understanding of biological processes. We argue that while a similar connection between information theory and evolutionary biology seems to b...