Neurologically inactive drugs are substances that do not have a direct effect on the central nervous system (CNS). They do not alter brain function or produce any significant psychoactive effects. Among the options provided, antihistamines are the drugs that are neurologically inactive.

1. Analgesics:
- Analgesics are drugs used to relieve pain. They work by inhibiting the transmission of pain signals in the peripheral nervous system and reducing inflammation.
- Examples of analgesics include nonsteroidal anti-inflammatory drugs (NSAIDs) like ibuprofen and acetaminophen (paracetamol).
- While analgesics primarily target pain receptors in the peripheral nervous system, some may have mild effects on the CNS, such as reducing fever or inducing drowsiness.

2. Barbiturates:
- Barbiturates are a class of drugs that act as central nervous system depressants. They are primarily used as sedatives, hypnotics, and anticonvulsants.
- Barbiturates exert their effects by enhancing the activity of the inhibitory neurotransmitter gamma-aminobutyric acid (GABA) in the brain, leading to sedation and relaxation.
- Due to their potent effects on the CNS, barbiturates are not considered neurologically inactive drugs.

3. Antipyretics:
- Antipyretics are drugs used to reduce fever. They work by inhibiting the production of prostaglandins, which are chemicals that cause fever.
- Common antipyretics include acetaminophen and nonsteroidal anti-inflammatory drugs (NSAIDs) such as ibuprofen.
- While antipyretics primarily act on the hypothalamus to lower body temperature, they may have mild effects on the CNS, such as reducing pain or inducing drowsiness.

4. Antihistamines:
- Antihistamines are drugs that block the effects of histamine, a chemical released by the immune system during allergic reactions.
- By blocking histamine receptors, antihistamines can relieve symptoms of allergies, such as itching, sneezing, and runny nose.
- Antihistamines are considered neurologically inactive because they do not directly affect brain function or produce sedation. However, some older generation antihistamines may have sedating side effects due to their ability to cross the blood-brain barrier.