The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease; the fluctuation theorem precisely quantifies this probability.
Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted . The theorem states that, in systems away from equilibrium over a finite time t, the ratio between the probability that takes on a value A and the probability that it takes the opposite value, −A, will be exponential in At.
In other words, for a finite non-equilibrium system in a finite time, the FT gives a precise mathematical expression for the probability that entropy will flow in a direction opposite to that dictated by the second law of thermodynamics.
Mathematically, the FT is expressed as:
This means that as the time or system size increases (since is extensive), the probability of observing an entropy production opposite to that dictated by the second law of thermodynamics decreases exponentially. The FT is one of the few expressions in non-equilibrium statistical mechanics that is valid far from equilibrium.
Note that the FT does not state that the second law of thermodynamics is wrong or invalid. The second law of thermodynamics is a statement about macroscopic systems. The FT is more general. It can be applied to both microscopic and macroscopic systems. When applied to macroscopic systems, the FT is equivalent to the Second Law of Thermodynamics.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
The heat death of the universe (also known as the Big Chill or Big Freeze) is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy, and will therefore be unable to sustain processes that increase entropy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium.
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease; the fluctuation theorem precisely quantifies this probability.
Maxwell's demon is a thought experiment that would hypothetically violate the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being who can play a game of skill with the molecules". Lord Kelvin would later call it a "demon". In the thought experiment, a demon controls a small massless door between two chambers of gas.
This first part of the course covers non-equilibrium statistical processes and the treatment of fluctuation dissipation relations by Einstein, Boltzmann and Kubo. Moreover, the fundamentals of Markov
The course is conceived in the perspective of understanding the fundamentals of spintronics. This implies learning about magnetism at the quantum mechanical level, mechanisms for spin relaxation and
We discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas an
We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.
We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.
Delves into the statistical aspects of quantum mechanics and its relation to stochastic processes, focusing on quantum optics and Markov jump processes.
Covers information measures like entropy, Kullback-Leibler divergence, and data processing inequality, along with probability kernels and mutual information.
We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the r
The Renyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field l
We investigate the ground state properties of large atoms and quantum dots described by a d-dimensional N-body Hamiltonian of confinement ZV. In atoms, d = 3 and V is the Coulomb interaction; in dots,