This paper provides a perspective on applying the concepts of information thermodynamics, developed recently in non-equilibrium statistical physics, to problems in theoretical neuroscience. Historically, information and energy in neuroscience have been treated separately, in contrast to physics approaches, where the relationship of entropy production with heat is a central idea. It is argued here that also in neural systems, information and energy can be considered within the same theoretical framework. Starting from basic ideas of thermodynamics and information theory on a classic Brownian particle, it is shown how noisy neural networks can infer its probabilistic motion. The decoding of the particle motion by neurons is performed with some accuracy, and it has some energy cost, and both can be determined using information thermodynamics. In a similar fashion, we also discuss how neural networks in the brain can learn the particle velocity and maintain that information in the weights of plastic synapses from a physical point of view. Generally, it is shown how the framework of stochastic and information thermodynamics can be used practically to study neural inference, learning, and information storing.

Theory of molecular machines. II. Energy dissipation from molecular machines. Single molecules perform a variety of tasks in cells, from replicating, controlling and translating the genetic material to sensing the outside environment. These operations all require that specific actions take place. In a sense, each molecule must make tiny decisions. To make a decision, each "molecular machine" must dissipate an energy Py in the presence of thermal noise Ny. The number of binary decisions that can be made by a machine which has dspace independently moving parts is the "machine capacity" Cy = dspace log2 [(Py + Ny)/Ny]. This formula is closely related to Shannon's channel capacity for communications systems, C = W log2 [(P + N)/N]. This paper shows that the minimum amount of energy that a molecular machine must dissipate in order to gain one bit of information is epsilon min = kB T ln (2) joules/bit. This equation is derived in two distinct ways. The first derivation begins with the Second Law of Thermodynamics, which shows that the statement that there is a minimum energy dissipation is a restatement of the Second Law of Thermodynamics.

the theory of complex systems, or in biology. Another objection is that evolution violates the second law of thermodynamics. The law states that "the Objections to evolution have been raised since evolutionary ideas came to prominence in the 19th century. When Charles Darwin published his 1859 book On the Origin of Species, his theory of evolution (the idea that species arose through descent with modification from a single common ancestor in a process driven by natural selection) initially met opposition from scientists with different theories, Another objection is that evolution violates the second law of thermodynamics. The law states that "the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium". In other words, an isolated system's entropy (a measure of the dispersal of energy in a physical system so that it is not available to do mechanical work) will tend to increase or stay the same, not decrease. Creationists argue that evolution violates this physical law by requiring an increase in order (i.e., a decrease in entropy). The claims have been criticized for ignoring that the second law only applies to isolated systems. Organisms are open systems as they constantly exchange energy and matter with their environment: for example animals eat food and excrete waste, and radiate and absorb heat. It is argued that the Sun-Earth-space system does not violate the second law because the enormous increase in entropy due to the Sun and Earth radiating into space dwarfs the local decrease in entropy caused by the existence and evolution of self-organizing life. Since the second law of thermodynamics has a precise mathematical definition, this argument can be analyzed quantitatively. This was done by physicist Daniel F. Styer, who concluded: "Quantitative estimates of the entropy involved in biological evolution demonstrate that there is no conflict between evolution and the second law of thermodynamics." In a published letter to the editor of The Mathematical Intelligencer titled "How anti-evolutionists abuse mathematics", mathematician Jason Rosenhouse stated: