the course of an extended computation, entropy must eventually be expelled to an outside environment. Equation Landauer's principle is based on the more general equation of Leon Brillouin (Brillouin 1956) estimating the energy of one bit of information as the minimum energy of a particle (e.g., photon) that has to overcome the energy of thermal noise to carry the information (formula below). The principle asserts that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer limit: where is the Boltzmann constant (approximately 1.38×10−23 J/K), is the temperature of the heat sink in kelvins, and is the natural logarithm of 2 (approximately 0.69315). After setting equal to room temperature 20 °C (293.15 K), we can get the Landauer limit of 0.0175 eV (2.805 zJ) per bit erased. The equation can be deduced from Boltzmann's entropy formula (), considering that is the number of states of the system, which in the case of a bit is 2, and the entropy is defined as . So the operation of erasing a single bit increases the entropy of a value of at least , emitting in the environment a quantity of energy equal or greater than . Challenges The principle is widely accepted as physical law, but in recent years it has been challenged for using circular reasoning and faulty assumptions, notably in Earman and Norton (1998), and subsequently in Shenker (2000) and Norton (2004, 2011), and defended by Bennett (2003), Ladyman et al. (2007), and by Jordan and Manikandan (2019). Other researchers have shown that Landauer's principle is a consequence of the second law of Thermodynamics and the entropy change associated with information gain. On the other hand, recent advances in non-equilibrium statistical physics have established that there is no a priori relationship between logical and thermodynamic reversibility. It is possible that a physical process is logically reversible but thermodynamically irreversible. It is also possible that a physical process is logically irreversible but thermodynamically reversible. At best, the benefits of implementing a computation with a logically reversible system are nuanced. In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle. However, according to Laszlo Kish (2016), their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode". See also Margolus–Levitin theorem Bremermann's limit